Scipy教程 - 统计函数库scipy.stats

客官°小女子只卖身不卖艺 2022-08-09 15:51 362阅读 0赞

http://[blog.csdn.net/pipisorry/article/details/49515215][blog.csdn.net_pipisorry_article_details_49515215]

## 统计函数Statistical functions(scipy.stats) ##

Python有一个很好的统计推断包。那就是scipy里面的stats。

Scipy的stats模块包含了多种概率分布的随机变量，随机变量分为连续的和离散的两种。  
所有的连续随机变量都是rv\_continuous的派生类的对象，而所有的离散随机变量都是 rv\_discrete的派生类的对象。

This module contains a large number of probability distributions as well as a growing library of statistical functions.

Each univariate distribution is an instance of a subclass of [rv\_continuous][rv_continuous]([rv\_discrete][rv_discrete] for discrete distributions):

<table> 
 <tbody> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.html#scipy.stats.rv_continuous" title="scipy.stats.rv_continuous" rel="nofollow">rv_continuous</a>([momtype,&nbsp;a,&nbsp;b,&nbsp;xtol,&nbsp;...])</td> 
 <td>A generic continuous random variable class meant for subclassing.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.html#scipy.stats.rv_discrete" title="scipy.stats.rv_discrete" rel="nofollow">rv_discrete</a>([a,&nbsp;b,&nbsp;name,&nbsp;badvalue,&nbsp;...])</td> 
 <td>A generic discrete random variable class meant for subclassing.</td> 
 </tr> 
 </tbody> 
</table>

[皮皮blog][blog]

# 连续分布及其相关的函数 #

## 连续分布 ##

<table> 
 <tbody> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.alpha.html#scipy.stats.alpha" title="scipy.stats.alpha" rel="nofollow">alpha</a></td> 
 <td>An alpha continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.anglit.html#scipy.stats.anglit" title="scipy.stats.anglit" rel="nofollow">anglit</a></td> 
 <td>An anglit continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.arcsine.html#scipy.stats.arcsine" title="scipy.stats.arcsine" rel="nofollow">arcsine</a></td> 
 <td>An arcsine continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.beta.html#scipy.stats.beta" title="scipy.stats.beta" rel="nofollow">beta</a></td> 
 <td>A beta continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.betaprime.html#scipy.stats.betaprime" title="scipy.stats.betaprime" rel="nofollow">betaprime</a></td> 
 <td>A beta prime continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.bradford.html#scipy.stats.bradford" title="scipy.stats.bradford" rel="nofollow">bradford</a></td> 
 <td>A Bradford continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.burr.html#scipy.stats.burr" title="scipy.stats.burr" rel="nofollow">burr</a></td> 
 <td>A Burr (Type III) continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.burr12.html#scipy.stats.burr12" title="scipy.stats.burr12" rel="nofollow">burr12</a></td> 
 <td>A Burr (Type XII) continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.cauchy.html#scipy.stats.cauchy" title="scipy.stats.cauchy" rel="nofollow">cauchy</a></td> 
 <td>A Cauchy continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chi.html#scipy.stats.chi" title="scipy.stats.chi" rel="nofollow">chi</a></td> 
 <td>A chi continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chi2.html#scipy.stats.chi2" title="scipy.stats.chi2" rel="nofollow">chi2</a></td> 
 <td>A chi-squared continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.cosine.html#scipy.stats.cosine" title="scipy.stats.cosine" rel="nofollow">cosine</a></td> 
 <td>A cosine continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.dgamma.html#scipy.stats.dgamma" title="scipy.stats.dgamma" rel="nofollow">dgamma</a></td> 
 <td>A double gamma continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.dweibull.html#scipy.stats.dweibull" title="scipy.stats.dweibull" rel="nofollow">dweibull</a></td> 
 <td>A double Weibull continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.erlang.html#scipy.stats.erlang" title="scipy.stats.erlang" rel="nofollow">erlang</a></td> 
 <td>An Erlang continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.expon.html#scipy.stats.expon" title="scipy.stats.expon" rel="nofollow">expon</a></td> 
 <td>An exponential continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.exponnorm.html#scipy.stats.exponnorm" title="scipy.stats.exponnorm" rel="nofollow">exponnorm</a></td> 
 <td>An exponentially modified Normal continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.exponweib.html#scipy.stats.exponweib" title="scipy.stats.exponweib" rel="nofollow">exponweib</a></td> 
 <td>An exponentiated Weibull continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.exponpow.html#scipy.stats.exponpow" title="scipy.stats.exponpow" rel="nofollow">exponpow</a></td> 
 <td>An exponential power continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.f.html#scipy.stats.f" title="scipy.stats.f" rel="nofollow">f</a></td> 
 <td>An F continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.fatiguelife.html#scipy.stats.fatiguelife" title="scipy.stats.fatiguelife" rel="nofollow">fatiguelife</a></td> 
 <td>A fatigue-life (Birnbaum-Saunders) continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.fisk.html#scipy.stats.fisk" title="scipy.stats.fisk" rel="nofollow">fisk</a></td> 
 <td>A Fisk continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.foldcauchy.html#scipy.stats.foldcauchy" title="scipy.stats.foldcauchy" rel="nofollow">foldcauchy</a></td> 
 <td>A folded Cauchy continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.foldnorm.html#scipy.stats.foldnorm" title="scipy.stats.foldnorm" rel="nofollow">foldnorm</a></td> 
 <td>A folded normal continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.frechet_r.html#scipy.stats.frechet_r" title="scipy.stats.frechet_r" rel="nofollow">frechet_r</a></td> 
 <td>A Frechet right (or Weibull minimum) continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.frechet_l.html#scipy.stats.frechet_l" title="scipy.stats.frechet_l" rel="nofollow">frechet_l</a></td> 
 <td>A Frechet left (or Weibull maximum) continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genlogistic.html#scipy.stats.genlogistic" title="scipy.stats.genlogistic" rel="nofollow">genlogistic</a></td> 
 <td>A generalized logistic continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gennorm.html#scipy.stats.gennorm" title="scipy.stats.gennorm" rel="nofollow">gennorm</a></td> 
 <td>A generalized normal continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genpareto.html#scipy.stats.genpareto" title="scipy.stats.genpareto" rel="nofollow">genpareto</a></td> 
 <td>A generalized Pareto continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genexpon.html#scipy.stats.genexpon" title="scipy.stats.genexpon" rel="nofollow">genexpon</a></td> 
 <td>A generalized exponential continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genextreme.html#scipy.stats.genextreme" title="scipy.stats.genextreme" rel="nofollow">genextreme</a></td> 
 <td>A generalized extreme value continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gausshyper.html#scipy.stats.gausshyper" title="scipy.stats.gausshyper" rel="nofollow">gausshyper</a></td> 
 <td>A Gauss hypergeometric continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gamma.html#scipy.stats.gamma" title="scipy.stats.gamma" rel="nofollow">gamma</a></td> 
 <td>A gamma continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gengamma.html#scipy.stats.gengamma" title="scipy.stats.gengamma" rel="nofollow">gengamma</a></td> 
 <td>A generalized gamma continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.genhalflogistic.html#scipy.stats.genhalflogistic" title="scipy.stats.genhalflogistic" rel="nofollow">genhalflogistic</a></td> 
 <td>A generalized half-logistic continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gilbrat.html#scipy.stats.gilbrat" title="scipy.stats.gilbrat" rel="nofollow">gilbrat</a></td> 
 <td>A Gilbrat continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gompertz.html#scipy.stats.gompertz" title="scipy.stats.gompertz" rel="nofollow">gompertz</a></td> 
 <td>A Gompertz (or truncated Gumbel) continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gumbel_r.html#scipy.stats.gumbel_r" title="scipy.stats.gumbel_r" rel="nofollow">gumbel_r</a></td> 
 <td>A right-skewed Gumbel continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gumbel_l.html#scipy.stats.gumbel_l" title="scipy.stats.gumbel_l" rel="nofollow">gumbel_l</a></td> 
 <td>A left-skewed Gumbel continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.halfcauchy.html#scipy.stats.halfcauchy" title="scipy.stats.halfcauchy" rel="nofollow">halfcauchy</a></td> 
 <td>A Half-Cauchy continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.halflogistic.html#scipy.stats.halflogistic" title="scipy.stats.halflogistic" rel="nofollow">halflogistic</a></td> 
 <td>A half-logistic continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.halfnorm.html#scipy.stats.halfnorm" title="scipy.stats.halfnorm" rel="nofollow">halfnorm</a></td> 
 <td>A half-normal continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.halfgennorm.html#scipy.stats.halfgennorm" title="scipy.stats.halfgennorm" rel="nofollow">halfgennorm</a></td> 
 <td>The upper half of a generalized normal continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.hypsecant.html#scipy.stats.hypsecant" title="scipy.stats.hypsecant" rel="nofollow">hypsecant</a></td> 
 <td>A hyperbolic secant continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.invgamma.html#scipy.stats.invgamma" title="scipy.stats.invgamma" rel="nofollow">invgamma</a></td> 
 <td>An inverted gamma continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.invgauss.html#scipy.stats.invgauss" title="scipy.stats.invgauss" rel="nofollow">invgauss</a></td> 
 <td>An inverse Gaussian continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.invweibull.html#scipy.stats.invweibull" title="scipy.stats.invweibull" rel="nofollow">invweibull</a></td> 
 <td>An inverted Weibull continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.johnsonsb.html#scipy.stats.johnsonsb" title="scipy.stats.johnsonsb" rel="nofollow">johnsonsb</a></td> 
 <td>A Johnson SB continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.johnsonsu.html#scipy.stats.johnsonsu" title="scipy.stats.johnsonsu" rel="nofollow">johnsonsu</a></td> 
 <td>A Johnson SU continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kappa4.html#scipy.stats.kappa4" title="scipy.stats.kappa4" rel="nofollow">kappa4</a></td> 
 <td>Kappa 4 parameter distribution.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kappa3.html#scipy.stats.kappa3" title="scipy.stats.kappa3" rel="nofollow">kappa3</a></td> 
 <td>Kappa 3 parameter distribution.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ksone.html#scipy.stats.ksone" title="scipy.stats.ksone" rel="nofollow">ksone</a></td> 
 <td>General Kolmogorov-Smirnov one-sided test.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kstwobign.html#scipy.stats.kstwobign" title="scipy.stats.kstwobign" rel="nofollow">kstwobign</a></td> 
 <td>Kolmogorov-Smirnov two-sided test for large N.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.laplace.html#scipy.stats.laplace" title="scipy.stats.laplace" rel="nofollow">laplace</a></td> 
 <td>A Laplace continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.levy.html#scipy.stats.levy" title="scipy.stats.levy" rel="nofollow">levy</a></td> 
 <td>A Levy continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.levy_l.html#scipy.stats.levy_l" title="scipy.stats.levy_l" rel="nofollow">levy_l</a></td> 
 <td>A left-skewed Levy continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.levy_stable.html#scipy.stats.levy_stable" title="scipy.stats.levy_stable" rel="nofollow">levy_stable</a></td> 
 <td>A Levy-stable continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.logistic.html#scipy.stats.logistic" title="scipy.stats.logistic" rel="nofollow">logistic</a></td> 
 <td>A logistic (or Sech-squared) continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.loggamma.html#scipy.stats.loggamma" title="scipy.stats.loggamma" rel="nofollow">loggamma</a></td> 
 <td>A log gamma continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.loglaplace.html#scipy.stats.loglaplace" title="scipy.stats.loglaplace" rel="nofollow">loglaplace</a></td> 
 <td>A log-Laplace continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.lognorm.html#scipy.stats.lognorm" title="scipy.stats.lognorm" rel="nofollow">lognorm</a></td> 
 <td>A lognormal continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.lomax.html#scipy.stats.lomax" title="scipy.stats.lomax" rel="nofollow">lomax</a></td> 
 <td>A Lomax (Pareto of the second kind) continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.maxwell.html#scipy.stats.maxwell" title="scipy.stats.maxwell" rel="nofollow">maxwell</a></td> 
 <td>A Maxwell continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.mielke.html#scipy.stats.mielke" title="scipy.stats.mielke" rel="nofollow">mielke</a></td> 
 <td>A Mielke’s Beta-Kappa continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.nakagami.html#scipy.stats.nakagami" title="scipy.stats.nakagami" rel="nofollow">nakagami</a></td> 
 <td>A Nakagami continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ncx2.html#scipy.stats.ncx2" title="scipy.stats.ncx2" rel="nofollow">ncx2</a></td> 
 <td>A non-central chi-squared continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ncf.html#scipy.stats.ncf" title="scipy.stats.ncf" rel="nofollow">ncf</a></td> 
 <td>A non-central F distribution continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.nct.html#scipy.stats.nct" title="scipy.stats.nct" rel="nofollow">nct</a></td> 
 <td>A non-central Student’s T continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.norm" title="scipy.stats.norm" rel="nofollow">norm</a></td> 
 <td>A normal continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pareto.html#scipy.stats.pareto" title="scipy.stats.pareto" rel="nofollow">pareto</a></td> 
 <td>A Pareto continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pearson3.html#scipy.stats.pearson3" title="scipy.stats.pearson3" rel="nofollow">pearson3</a></td> 
 <td>A pearson type III continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.powerlaw.html#scipy.stats.powerlaw" title="scipy.stats.powerlaw" rel="nofollow">powerlaw</a></td> 
 <td>A power-function continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.powerlognorm.html#scipy.stats.powerlognorm" title="scipy.stats.powerlognorm" rel="nofollow">powerlognorm</a></td> 
 <td>A power log-normal continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.powernorm.html#scipy.stats.powernorm" title="scipy.stats.powernorm" rel="nofollow">powernorm</a></td> 
 <td>A power normal continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rdist.html#scipy.stats.rdist" title="scipy.stats.rdist" rel="nofollow">rdist</a></td> 
 <td>An R-distributed continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.reciprocal.html#scipy.stats.reciprocal" title="scipy.stats.reciprocal" rel="nofollow">reciprocal</a></td> 
 <td>A reciprocal continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rayleigh.html#scipy.stats.rayleigh" title="scipy.stats.rayleigh" rel="nofollow">rayleigh</a></td> 
 <td>A Rayleigh continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rice.html#scipy.stats.rice" title="scipy.stats.rice" rel="nofollow">rice</a></td> 
 <td>A Rice continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.recipinvgauss.html#scipy.stats.recipinvgauss" title="scipy.stats.recipinvgauss" rel="nofollow">recipinvgauss</a></td> 
 <td>A reciprocal inverse Gaussian continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.semicircular.html#scipy.stats.semicircular" title="scipy.stats.semicircular" rel="nofollow">semicircular</a></td> 
 <td>A semicircular continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.skewnorm.html#scipy.stats.skewnorm" title="scipy.stats.skewnorm" rel="nofollow">skewnorm</a></td> 
 <td>A skew-normal random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.t.html#scipy.stats.t" title="scipy.stats.t" rel="nofollow">t</a></td> 
 <td>A Student’s T continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.trapz.html#scipy.stats.trapz" title="scipy.stats.trapz" rel="nofollow">trapz</a></td> 
 <td>A trapezoidal continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.triang.html#scipy.stats.triang" title="scipy.stats.triang" rel="nofollow">triang</a></td> 
 <td>A triangular continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.truncexpon.html#scipy.stats.truncexpon" title="scipy.stats.truncexpon" rel="nofollow">truncexpon</a></td> 
 <td>A truncated exponential continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.truncnorm.html#scipy.stats.truncnorm" title="scipy.stats.truncnorm" rel="nofollow">truncnorm</a></td> 
 <td>A truncated normal continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.tukeylambda.html#scipy.stats.tukeylambda" title="scipy.stats.tukeylambda" rel="nofollow">tukeylambda</a></td> 
 <td>A Tukey-Lamdba continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.uniform.html#scipy.stats.uniform" title="scipy.stats.uniform" rel="nofollow">uniform</a></td> 
 <td>A uniform continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.vonmises.html#scipy.stats.vonmises" title="scipy.stats.vonmises" rel="nofollow">vonmises</a></td> 
 <td>A Von Mises continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.vonmises_line.html#scipy.stats.vonmises_line" title="scipy.stats.vonmises_line" rel="nofollow">vonmises_line</a></td> 
 <td>A Von Mises continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.wald.html#scipy.stats.wald" title="scipy.stats.wald" rel="nofollow">wald</a></td> 
 <td>A Wald continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.weibull_min.html#scipy.stats.weibull_min" title="scipy.stats.weibull_min" rel="nofollow">weibull_min</a></td> 
 <td>A Frechet right (or Weibull minimum) continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.weibull_max.html#scipy.stats.weibull_max" title="scipy.stats.weibull_max" rel="nofollow">weibull_max</a></td> 
 <td>A Frechet left (or Weibull maximum) continuous random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.wrapcauchy.html#scipy.stats.wrapcauchy" title="scipy.stats.wrapcauchy" rel="nofollow">wrapcauchy</a></td> 
 <td>A wrapped Cauchy continuous random variable.</td> 
 </tr> 
 </tbody> 
</table>

## 连续随机变量对象的方法    ##

<table> 
 <tbody> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.rvs.html#scipy.stats.rv_continuous.rvs" title="scipy.stats.rv_continuous.rvs" rel="nofollow">rvs</a>(*args,&nbsp;**kwds)</td> 
 <td>Random variates of given type.产生服从这种分布的一个样本，对随机变量进行随机取值，可以通过size参数指定输出的数组大小。</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.pdf.html#scipy.stats.rv_continuous.pdf" title="scipy.stats.rv_continuous.pdf" rel="nofollow">pdf</a>(x,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>Probability density function at x of the given RV.随机变量的概率密度函数。产生对应x的这种分布的y值。</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.logpdf.html#scipy.stats.rv_continuous.logpdf" title="scipy.stats.rv_continuous.logpdf" rel="nofollow">logpdf</a>(x,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>Log of the probability density function at x of the given RV.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.cdf.html#scipy.stats.rv_continuous.cdf" title="scipy.stats.rv_continuous.cdf" rel="nofollow">cdf</a>(x,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>Cumulative distribution function of the given RV.随机变量的累积分布函数，它是概率密度函数的积分（也就是x时p(X&lt;x)的概率）。产生对应x的这种分布的累积分布函数的值。</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.logcdf.html#scipy.stats.rv_continuous.logcdf" title="scipy.stats.rv_continuous.logcdf" rel="nofollow">logcdf</a>(x,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>Log of the cumulative distribution function at x of the given RV.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.sf.html#scipy.stats.rv_continuous.sf" title="scipy.stats.rv_continuous.sf" rel="nofollow">sf</a>(x,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>Survival function (1 - <a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.cdf.html#scipy.stats.rv_continuous.cdf" title="scipy.stats.rv_continuous.cdf" rel="nofollow">cdf</a>) at x of the given RV.随机变量的生存函数，它的值是1-cdf(t)。</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.logsf.html#scipy.stats.rv_continuous.logsf" title="scipy.stats.rv_continuous.logsf" rel="nofollow">logsf</a>(x,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>Log of the survival function of the given RV.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.ppf.html#scipy.stats.rv_continuous.ppf" title="scipy.stats.rv_continuous.ppf" rel="nofollow">ppf</a>(q,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>Percent point function (inverse of <a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.cdf.html#scipy.stats.rv_continuous.cdf" title="scipy.stats.rv_continuous.cdf" rel="nofollow">cdf</a>) at q of the given RV.累积分布函数的反函数。q=0.01时，ppf就是p(X&lt;x)=0.01时的x值。</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.isf.html#scipy.stats.rv_continuous.isf" title="scipy.stats.rv_continuous.isf" rel="nofollow">isf</a>(q,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>Inverse survival function (inverse of <a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.sf.html#scipy.stats.rv_continuous.sf" title="scipy.stats.rv_continuous.sf" rel="nofollow">sf</a>) at q of the given RV.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.moment.html#scipy.stats.rv_continuous.moment" title="scipy.stats.rv_continuous.moment" rel="nofollow">moment</a>(n,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>n-th order non-central moment of distribution.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.stats.html#scipy.stats.rv_continuous.stats" title="scipy.stats.rv_continuous.stats" rel="nofollow">stats</a>(*args,&nbsp;**kwds)</td> 
 <td>Some statistics of the given RV.计算随机变量的期望值和方差。</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.entropy.html#scipy.stats.rv_continuous.entropy" title="scipy.stats.rv_continuous.entropy" rel="nofollow">entropy</a>(*args,&nbsp;**kwds)</td> 
 <td>Differential entropy of the RV.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.expect.html#scipy.stats.rv_continuous.expect" title="scipy.stats.rv_continuous.expect" rel="nofollow">expect</a>([func,&nbsp;args,&nbsp;loc,&nbsp;scale,&nbsp;lb,&nbsp;ub,&nbsp;...])</td> 
 <td>Calculate expected value of a function with respect to the distribution.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.median.html#scipy.stats.rv_continuous.median" title="scipy.stats.rv_continuous.median" rel="nofollow">median</a>(*args,&nbsp;**kwds)</td> 
 <td>Median of the distribution.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.mean.html#scipy.stats.rv_continuous.mean" title="scipy.stats.rv_continuous.mean" rel="nofollow">mean</a>(*args,&nbsp;**kwds)</td> 
 <td>Mean of the distribution.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.std.html#scipy.stats.rv_continuous.std" title="scipy.stats.rv_continuous.std" rel="nofollow">std</a>(*args,&nbsp;**kwds)</td> 
 <td>Standard deviation of the distribution.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.var.html#scipy.stats.rv_continuous.var" title="scipy.stats.rv_continuous.var" rel="nofollow">var</a>(*args,&nbsp;**kwds)</td> 
 <td>Variance of the distribution.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.interval.html#scipy.stats.rv_continuous.interval" title="scipy.stats.rv_continuous.interval" rel="nofollow">interval</a>(alpha,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>Confidence interval with equal areas around the median.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.__call__.html#scipy.stats.rv_continuous.__call__" title="scipy.stats.rv_continuous.__call__" rel="nofollow">__call__</a>(*args,&nbsp;**kwds)</td> 
 <td>Freeze the distribution for the given arguments.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.fit.html#scipy.stats.rv_continuous.fit" title="scipy.stats.rv_continuous.fit" rel="nofollow">fit</a>(data,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>Return MLEs for shape, location, and scale parameters from data.对一组随机取样进行拟合，找出最适合取样数据的概率密度函数的系数。如stats.norm.fit(x)就是将x看成是某个norm分布的抽样，求出其最好的拟合参数（mean, std）。</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.fit_loc_scale.html#scipy.stats.rv_continuous.fit_loc_scale" title="scipy.stats.rv_continuous.fit_loc_scale" rel="nofollow">fit_loc_scale</a>(data,&nbsp;*args)</td> 
 <td>Estimate loc and scale parameters from data using 1st and 2nd moments.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.nnlf.html#scipy.stats.rv_continuous.nnlf" title="scipy.stats.rv_continuous.nnlf" rel="nofollow">nnlf</a>(theta,&nbsp;x)</td> 
 <td>Return negative loglikelihood function.</td> 
 </tr> 
 </tbody> 
</table>

\[ [Continuous distributions][]\]

\[[scipy.stats.rv\_continuous][rv_continuous]\]

## 多变量分布Multivariate distributions    ##

<table> 
 <tbody> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.multivariate_normal.html#scipy.stats.multivariate_normal" title="scipy.stats.multivariate_normal" rel="nofollow">multivariate_normal</a></td> 
 <td>A multivariate normal random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.matrix_normal.html#scipy.stats.matrix_normal" title="scipy.stats.matrix_normal" rel="nofollow">matrix_normal</a></td> 
 <td>A matrix normal random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.dirichlet.html#scipy.stats.dirichlet" title="scipy.stats.dirichlet" rel="nofollow">dirichlet</a></td> 
 <td>A Dirichlet random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.wishart.html#scipy.stats.wishart" title="scipy.stats.wishart" rel="nofollow">wishart</a></td> 
 <td>A Wishart random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.invwishart.html#scipy.stats.invwishart" title="scipy.stats.invwishart" rel="nofollow">invwishart</a></td> 
 <td>An inverse Wishart random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.special_ortho_group.html#scipy.stats.special_ortho_group" title="scipy.stats.special_ortho_group" rel="nofollow">special_ortho_group</a></td> 
 <td>A matrix-valued SO(N) random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ortho_group.html#scipy.stats.ortho_group" title="scipy.stats.ortho_group" rel="nofollow">ortho_group</a></td> 
 <td>A matrix-valued O(N) random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.random_correlation.html#scipy.stats.random_correlation" title="scipy.stats.random_correlation" rel="nofollow">random_correlation</a></td> 
 <td>A random correlation matrix.</td> 
 </tr> 
 </tbody> 
</table>

### multivariate\_normal ###

>>> x, y = np.mgrid\[-1:1:.01, -1:1:.01\]  
>>> pos = np.dstack((x, y))   \#二维坐标组合成三维坐标点坐标  
>>> rv = multivariate\_normal(\[0.5, -0.2\], \[\[2.0, 0.3\], \[0.3, 0.5\]\])  
>>> rv.pdf(pos)  \#接受的参数是三维数据，第三维代表一个数据坐标，1、2维代表网格坐标位置。

[皮皮blog][blog]

# 离散分布及其相关的函数 #

当分布函数的值域为离散时，称之为离散概率分布。例如投掷有6个面的骰子时，只能获得1到6的整数，因此得到的概率分布为离散的。

对于离散随机分布，通常使用概率质量函数(PMF)描述其分布情况。在stats库中所有描述离散分布的随机变量都从rv\_discrete类继承。

### 直接用rv\_discrete 类自定义离散概率分布 ###

stats.rv\_discrete(values=(x,p))中的参数表示随机变量x和其对应的概率。

设有一个不均匀的骰子，各点出现的概率不相等。可以用下面的数组x保存骰子的所有可能值，数组p保存每个值出现的概率：  
>>> x = range(1,7)  
>>> p = (0.4, 0.2, 0.1, 0.1, 0.1, 0.1)  
用下面的语句定义表示这个特殊骰子的随机变量，并调用其rvs()方法投掷此骰子20次，获得符合概率p的随机数:  
>>> dice = stats.rv\_discrete(values=(x,p))  
>>> dice.rvs(size=20)  
Array(\[2, 5, 1, 2, 1, 1, 2, 4, 1, 3, 1, 1, 4, 3, 1, 1, 1, 2, 6, 4\])

from scipy import stats
    import numpy as np
    import matplotlib.pyplot as plt
    fs_meetsig = np.random.random(30)
    fs_xk = np.sort(fs_meetsig)
    fs_pk = np.ones_like(fs_xk) / len(fs_xk)
    fs_rv_dist = stats.rv_discrete(name='fs_rv_dist', values=(fs_xk, fs_pk))
    
    plt.plot(fs_xk, fs_rv_dist.cdf(fs_xk), 'b-', ms=12, mec='r', label='friend')
    plt.show()

\[rv\_discrete [Examples][]\]

### 离散分布 ###

<table> 
 <tbody> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.bernoulli.html#scipy.stats.bernoulli" title="scipy.stats.bernoulli" rel="nofollow">bernoulli</a></td> 
 <td>A Bernoulli discrete random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.binom.html#scipy.stats.binom" title="scipy.stats.binom" rel="nofollow">binom</a></td> 
 <td>A binomial discrete random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.boltzmann.html#scipy.stats.boltzmann" title="scipy.stats.boltzmann" rel="nofollow">boltzmann</a></td> 
 <td>A Boltzmann (Truncated Discrete Exponential) random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.dlaplace.html#scipy.stats.dlaplace" title="scipy.stats.dlaplace" rel="nofollow">dlaplace</a></td> 
 <td>A Laplacian discrete random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.geom.html#scipy.stats.geom" title="scipy.stats.geom" rel="nofollow">geom</a></td> 
 <td>A geometric discrete random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.hypergeom.html#scipy.stats.hypergeom" title="scipy.stats.hypergeom" rel="nofollow">hypergeom</a></td> 
 <td>A hypergeometric discrete random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.logser.html#scipy.stats.logser" title="scipy.stats.logser" rel="nofollow">logser</a></td> 
 <td>A Logarithmic (Log-Series, Series) discrete random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.nbinom.html#scipy.stats.nbinom" title="scipy.stats.nbinom" rel="nofollow">nbinom</a></td> 
 <td>A negative binomial discrete random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.planck.html#scipy.stats.planck" title="scipy.stats.planck" rel="nofollow">planck</a></td> 
 <td>A Planck discrete exponential random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.poisson.html#scipy.stats.poisson" title="scipy.stats.poisson" rel="nofollow">poisson</a></td> 
 <td>A Poisson discrete random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.randint.html#scipy.stats.randint" title="scipy.stats.randint" rel="nofollow">randint</a></td> 
 <td>A uniform discrete random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.skellam.html#scipy.stats.skellam" title="scipy.stats.skellam" rel="nofollow">skellam</a></td> 
 <td>A Skellam discrete random variable.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.zipf.html#scipy.stats.zipf" title="scipy.stats.zipf" rel="nofollow">zipf</a></td> 
 <td>A Zipf discrete random variable.</td> 
 </tr> 
 </tbody> 
</table>

## 离散分布的函数 ##

<table> 
 <tbody> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.rvs.html#scipy.stats.rv_discrete.rvs" title="scipy.stats.rv_discrete.rvs" rel="nofollow">rvs</a>(*args,&nbsp;**kwargs)</td> 
 <td>Random variates of given type.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.pmf.html#scipy.stats.rv_discrete.pmf" title="scipy.stats.rv_discrete.pmf" rel="nofollow">pmf</a>(k,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>Probability mass function at k of the given RV.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.logpmf.html#scipy.stats.rv_discrete.logpmf" title="scipy.stats.rv_discrete.logpmf" rel="nofollow">logpmf</a>(k,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>Log of the probability mass function at k of the given RV.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.cdf.html#scipy.stats.rv_discrete.cdf" title="scipy.stats.rv_discrete.cdf" rel="nofollow">cdf</a>(k,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>Cumulative distribution function of the given RV.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.logcdf.html#scipy.stats.rv_discrete.logcdf" title="scipy.stats.rv_discrete.logcdf" rel="nofollow">logcdf</a>(k,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>Log of the cumulative distribution function at k of the given RV.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.sf.html#scipy.stats.rv_discrete.sf" title="scipy.stats.rv_discrete.sf" rel="nofollow">sf</a>(k,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>Survival function (1 - <a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.cdf.html#scipy.stats.rv_discrete.cdf" title="scipy.stats.rv_discrete.cdf" rel="nofollow">cdf</a>) at k of the given RV.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.logsf.html#scipy.stats.rv_discrete.logsf" title="scipy.stats.rv_discrete.logsf" rel="nofollow">logsf</a>(k,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>Log of the survival function of the given RV.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.ppf.html#scipy.stats.rv_discrete.ppf" title="scipy.stats.rv_discrete.ppf" rel="nofollow">ppf</a>(q,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>Percent point function (inverse of <a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.cdf.html#scipy.stats.rv_discrete.cdf" title="scipy.stats.rv_discrete.cdf" rel="nofollow">cdf</a>) at q of the given RV.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.isf.html#scipy.stats.rv_discrete.isf" title="scipy.stats.rv_discrete.isf" rel="nofollow">isf</a>(q,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>Inverse survival function (inverse of <a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.sf.html#scipy.stats.rv_discrete.sf" title="scipy.stats.rv_discrete.sf" rel="nofollow">sf</a>) at q of the given RV.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.moment.html#scipy.stats.rv_discrete.moment" title="scipy.stats.rv_discrete.moment" rel="nofollow">moment</a>(n,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>n-th order non-central moment of distribution.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.stats.html#scipy.stats.rv_discrete.stats" title="scipy.stats.rv_discrete.stats" rel="nofollow">stats</a>(*args,&nbsp;**kwds)</td> 
 <td>Some statistics of the given RV.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.entropy.html#scipy.stats.rv_discrete.entropy" title="scipy.stats.rv_discrete.entropy" rel="nofollow">entropy</a>(*args,&nbsp;**kwds)</td> 
 <td>Differential entropy of the RV.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.expect.html#scipy.stats.rv_discrete.expect" title="scipy.stats.rv_discrete.expect" rel="nofollow">expect</a>([func,&nbsp;args,&nbsp;loc,&nbsp;lb,&nbsp;ub,&nbsp;...])</td> 
 <td>Calculate expected value of a function with respect to the distribution for discrete distribution.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.median.html#scipy.stats.rv_discrete.median" title="scipy.stats.rv_discrete.median" rel="nofollow">median</a>(*args,&nbsp;**kwds)</td> 
 <td>Median of the distribution.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.mean.html#scipy.stats.rv_discrete.mean" title="scipy.stats.rv_discrete.mean" rel="nofollow">mean</a>(*args,&nbsp;**kwds)</td> 
 <td>Mean of the distribution.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.std.html#scipy.stats.rv_discrete.std" title="scipy.stats.rv_discrete.std" rel="nofollow">std</a>(*args,&nbsp;**kwds)</td> 
 <td>Standard deviation of the distribution.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.var.html#scipy.stats.rv_discrete.var" title="scipy.stats.rv_discrete.var" rel="nofollow">var</a>(*args,&nbsp;**kwds)</td> 
 <td>Variance of the distribution.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.interval.html#scipy.stats.rv_discrete.interval" title="scipy.stats.rv_discrete.interval" rel="nofollow">interval</a>(alpha,&nbsp;*args,&nbsp;**kwds)</td> 
 <td>Confidence interval with equal areas around the median.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.__call__.html#scipy.stats.rv_discrete.__call__" title="scipy.stats.rv_discrete.__call__" rel="nofollow">__call__</a>(*args,&nbsp;**kwds)</td> 
 <td>Freeze the distribution for the given arguments.</td> 
 </tr> 
 </tbody> 
</table>

[皮皮blog][blog]

# 统计函数Statistical functions #

\{scipy.stats顶层函数，可以应用于很多分布的函数\}

Several of these functions have a similar version in scipy.stats.mstats which work for masked arrays.

<table> 
 <tbody> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.describe.html#scipy.stats.describe" title="scipy.stats.describe" rel="nofollow">describe</a>(a[,&nbsp;axis,&nbsp;ddof,&nbsp;bias,&nbsp;nan_policy])</td> 
 <td>Computes several descriptive statistics of the passed array.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gmean.html#scipy.stats.gmean" title="scipy.stats.gmean" rel="nofollow">gmean</a>(a[,&nbsp;axis,&nbsp;dtype])</td> 
 <td>Compute the geometric mean along the specified axis.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.hmean.html#scipy.stats.hmean" title="scipy.stats.hmean" rel="nofollow">hmean</a>(a[,&nbsp;axis,&nbsp;dtype])</td> 
 <td>Calculates the harmonic mean along the specified axis.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kurtosis.html#scipy.stats.kurtosis" title="scipy.stats.kurtosis" rel="nofollow">kurtosis</a>(a[,&nbsp;axis,&nbsp;fisher,&nbsp;bias,&nbsp;nan_policy])</td> 
 <td>Computes the kurtosis (Fisher or Pearson) of a dataset.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kurtosistest.html#scipy.stats.kurtosistest" title="scipy.stats.kurtosistest" rel="nofollow">kurtosistest</a>(a[,&nbsp;axis,&nbsp;nan_policy])</td> 
 <td>Tests whether a dataset has normal kurtosis</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.mode.html#scipy.stats.mode" title="scipy.stats.mode" rel="nofollow">mode</a>(a[,&nbsp;axis,&nbsp;nan_policy])</td> 
 <td>Returns an array of the modal (most common) value in the passed array.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.moment.html#scipy.stats.moment" title="scipy.stats.moment" rel="nofollow">moment</a>(a[,&nbsp;moment,&nbsp;axis,&nbsp;nan_policy])</td> 
 <td>Calculates the nth moment about the mean for a sample.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.normaltest.html#scipy.stats.normaltest" title="scipy.stats.normaltest" rel="nofollow">normaltest</a>(a[,&nbsp;axis,&nbsp;nan_policy])</td> 
 <td>Tests whether a sample differs from a normal distribution.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.skew.html#scipy.stats.skew" title="scipy.stats.skew" rel="nofollow">skew</a>(a[,&nbsp;axis,&nbsp;bias,&nbsp;nan_policy])</td> 
 <td>Computes the skewness of a data set.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.skewtest.html#scipy.stats.skewtest" title="scipy.stats.skewtest" rel="nofollow">skewtest</a>(a[,&nbsp;axis,&nbsp;nan_policy])</td> 
 <td>Tests whether the skew is different from the normal distribution.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kstat.html#scipy.stats.kstat" title="scipy.stats.kstat" rel="nofollow">kstat</a>(data[,&nbsp;n])</td> 
 <td>Return the nth k-statistic (1&lt;=n&lt;=4 so far).</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kstatvar.html#scipy.stats.kstatvar" title="scipy.stats.kstatvar" rel="nofollow">kstatvar</a>(data[,&nbsp;n])</td> 
 <td>Returns an unbiased estimator of the variance of the k-statistic.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.tmean.html#scipy.stats.tmean" title="scipy.stats.tmean" rel="nofollow">tmean</a>(a[,&nbsp;limits,&nbsp;inclusive,&nbsp;axis])</td> 
 <td>Compute the trimmed mean.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.tvar.html#scipy.stats.tvar" title="scipy.stats.tvar" rel="nofollow">tvar</a>(a[,&nbsp;limits,&nbsp;inclusive,&nbsp;axis,&nbsp;ddof])</td> 
 <td>Compute the trimmed variance</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.tmin.html#scipy.stats.tmin" title="scipy.stats.tmin" rel="nofollow">tmin</a>(a[,&nbsp;lowerlimit,&nbsp;axis,&nbsp;inclusive,&nbsp;...])</td> 
 <td>Compute the trimmed minimum</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.tmax.html#scipy.stats.tmax" title="scipy.stats.tmax" rel="nofollow">tmax</a>(a[,&nbsp;upperlimit,&nbsp;axis,&nbsp;inclusive,&nbsp;...])</td> 
 <td>Compute the trimmed maximum</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.tstd.html#scipy.stats.tstd" title="scipy.stats.tstd" rel="nofollow">tstd</a>(a[,&nbsp;limits,&nbsp;inclusive,&nbsp;axis,&nbsp;ddof])</td> 
 <td>Compute the trimmed sample standard deviation</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.tsem.html#scipy.stats.tsem" title="scipy.stats.tsem" rel="nofollow">tsem</a>(a[,&nbsp;limits,&nbsp;inclusive,&nbsp;axis,&nbsp;ddof])</td> 
 <td>Compute the trimmed standard error of the mean.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.variation.html#scipy.stats.variation" title="scipy.stats.variation" rel="nofollow">variation</a>(a[,&nbsp;axis,&nbsp;nan_policy])</td> 
 <td>Computes the coefficient of variation, the ratio of the biased standard deviation to the mean.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.find_repeats.html#scipy.stats.find_repeats" title="scipy.stats.find_repeats" rel="nofollow">find_repeats</a>(arr)</td> 
 <td>Find repeats and repeat counts.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.trim_mean.html#scipy.stats.trim_mean" title="scipy.stats.trim_mean" rel="nofollow">trim_mean</a>(a,&nbsp;proportiontocut[,&nbsp;axis])</td> 
 <td>Return mean of array after trimming distribution from both tails.</td> 
 </tr> 
 </tbody> 
</table>

<table> 
 <tbody> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.cumfreq.html#scipy.stats.cumfreq" title="scipy.stats.cumfreq" rel="nofollow">cumfreq</a>(a[,&nbsp;numbins,&nbsp;defaultreallimits,&nbsp;weights])</td> 
 <td>Returns a cumulative frequency histogram, using the histogram function.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.histogram2.html#scipy.stats.histogram2" title="scipy.stats.histogram2" rel="nofollow">histogram2</a>(*args,&nbsp;**kwds)</td> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.histogram2.html#scipy.stats.histogram2" title="scipy.stats.histogram2" rel="nofollow">histogram2</a> is deprecated!</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.histogram.html#scipy.stats.histogram" title="scipy.stats.histogram" rel="nofollow">histogram</a>(*args,&nbsp;**kwds)</td> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.histogram.html#scipy.stats.histogram" title="scipy.stats.histogram" rel="nofollow">histogram</a> is deprecated!</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.itemfreq.html#scipy.stats.itemfreq" title="scipy.stats.itemfreq" rel="nofollow">itemfreq</a>(a)</td> 
 <td>Returns a 2-D array of item frequencies.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.percentileofscore.html#scipy.stats.percentileofscore" title="scipy.stats.percentileofscore" rel="nofollow">percentileofscore</a>(a,&nbsp;score[,&nbsp;kind])</td> 
 <td>The percentile rank of a score relative to a list of scores.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.scoreatpercentile.html#scipy.stats.scoreatpercentile" title="scipy.stats.scoreatpercentile" rel="nofollow">scoreatpercentile</a>(a,&nbsp;per[,&nbsp;limit,&nbsp;...])</td> 
 <td>Calculate the score at a given percentile of the input sequence.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.relfreq.html#scipy.stats.relfreq" title="scipy.stats.relfreq" rel="nofollow">relfreq</a>(a[,&nbsp;numbins,&nbsp;defaultreallimits,&nbsp;weights])</td> 
 <td>Returns a relative frequency histogram, using the histogram function.</td> 
 </tr> 
 </tbody> 
</table>

<table> 
 <tbody> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.binned_statistic.html#scipy.stats.binned_statistic" title="scipy.stats.binned_statistic" rel="nofollow">binned_statistic</a>(x,&nbsp;values[,&nbsp;statistic,&nbsp;...])</td> 
 <td>Compute a binned statistic for one or more sets of data.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.binned_statistic_2d.html#scipy.stats.binned_statistic_2d" title="scipy.stats.binned_statistic_2d" rel="nofollow">binned_statistic_2d</a>(x,&nbsp;y,&nbsp;values[,&nbsp;...])</td> 
 <td>Compute a bidimensional binned statistic for one or more sets of data.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.binned_statistic_dd.html#scipy.stats.binned_statistic_dd" title="scipy.stats.binned_statistic_dd" rel="nofollow">binned_statistic_dd</a>(sample,&nbsp;values[,&nbsp;...])</td> 
 <td>Compute a multidimensional binned statistic for a set of data.</td> 
 </tr> 
 </tbody> 
</table>

<table> 
 <tbody> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.obrientransform.html#scipy.stats.obrientransform" title="scipy.stats.obrientransform" rel="nofollow">obrientransform</a>(*args)</td> 
 <td>Computes the O’Brien transform on input data (any number of arrays).</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.signaltonoise.html#scipy.stats.signaltonoise" title="scipy.stats.signaltonoise" rel="nofollow">signaltonoise</a>(*args,&nbsp;**kwds)</td> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.signaltonoise.html#scipy.stats.signaltonoise" title="scipy.stats.signaltonoise" rel="nofollow">signaltonoise</a> is deprecated!</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.bayes_mvs.html#scipy.stats.bayes_mvs" title="scipy.stats.bayes_mvs" rel="nofollow">bayes_mvs</a>(data[,&nbsp;alpha])</td> 
 <td>Bayesian confidence intervals for the mean, var, and std.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.mvsdist.html#scipy.stats.mvsdist" title="scipy.stats.mvsdist" rel="nofollow">mvsdist</a>(data)</td> 
 <td>‘Frozen’ distributions for mean, variance, and standard deviation of data.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.sem.html#scipy.stats.sem" title="scipy.stats.sem" rel="nofollow">sem</a>(a[,&nbsp;axis,&nbsp;ddof,&nbsp;nan_policy])</td> 
 <td>Calculates the standard error of the mean (or standard error of measurement) of the values in the input array.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.zmap.html#scipy.stats.zmap" title="scipy.stats.zmap" rel="nofollow">zmap</a>(scores,&nbsp;compare[,&nbsp;axis,&nbsp;ddof])</td> 
 <td>Calculates the relative z-scores.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.zscore.html#scipy.stats.zscore" title="scipy.stats.zscore" rel="nofollow">zscore</a>(a[,&nbsp;axis,&nbsp;ddof])</td> 
 <td>Calculates the z score of each value in the sample, relative to the sample mean and standard deviation.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.iqr.html#scipy.stats.iqr" title="scipy.stats.iqr" rel="nofollow">iqr</a>(x[,&nbsp;axis,&nbsp;rng,&nbsp;scale,&nbsp;nan_policy,&nbsp;...])</td> 
 <td>Compute the interquartile range of the data along the specified axis.</td> 
 </tr> 
 </tbody> 
</table>

<table> 
 <tbody> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.sigmaclip.html#scipy.stats.sigmaclip" title="scipy.stats.sigmaclip" rel="nofollow">sigmaclip</a>(a[,&nbsp;low,&nbsp;high])</td> 
 <td>Iterative sigma-clipping of array elements.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.threshold.html#scipy.stats.threshold" title="scipy.stats.threshold" rel="nofollow">threshold</a>(*args,&nbsp;**kwds)</td> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.threshold.html#scipy.stats.threshold" title="scipy.stats.threshold" rel="nofollow">threshold</a> is deprecated!</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.trimboth.html#scipy.stats.trimboth" title="scipy.stats.trimboth" rel="nofollow">trimboth</a>(a,&nbsp;proportiontocut[,&nbsp;axis])</td> 
 <td>Slices off a proportion of items from both ends of an array.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.trim1.html#scipy.stats.trim1" title="scipy.stats.trim1" rel="nofollow">trim1</a>(a,&nbsp;proportiontocut[,&nbsp;tail,&nbsp;axis])</td> 
 <td>Slices off a proportion from ONE end of the passed array distribution.</td> 
 </tr> 
 </tbody> 
</table>

<table> 
 <tbody> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.f_oneway.html#scipy.stats.f_oneway" title="scipy.stats.f_oneway" rel="nofollow">f_oneway</a>(*args)</td> 
 <td>Performs a 1-way ANOVA.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pearsonr.html#scipy.stats.pearsonr" title="scipy.stats.pearsonr" rel="nofollow">pearsonr</a>(x,&nbsp;y)</td> 
 <td>Calculates a Pearson correlation coefficient and the p-value for testing non-correlation.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.spearmanr.html#scipy.stats.spearmanr" title="scipy.stats.spearmanr" rel="nofollow">spearmanr</a>(a[,&nbsp;b,&nbsp;axis,&nbsp;nan_policy])</td> 
 <td>Calculates a Spearman rank-order correlation coefficient and the p-value to test for non-correlation.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pointbiserialr.html#scipy.stats.pointbiserialr" title="scipy.stats.pointbiserialr" rel="nofollow">pointbiserialr</a>(x,&nbsp;y)</td> 
 <td>Calculates a point biserial correlation coefficient and its p-value.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kendalltau.html#scipy.stats.kendalltau" title="scipy.stats.kendalltau" rel="nofollow">kendalltau</a>(x,&nbsp;y[,&nbsp;initial_lexsort,&nbsp;nan_policy])</td> 
 <td>Calculates Kendall’s tau, a correlation measure for ordinal data.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.linregress.html#scipy.stats.linregress" title="scipy.stats.linregress" rel="nofollow">linregress</a>(x[,&nbsp;y])</td> 
 <td>Calculate a linear least-squares regression for two sets of measurements.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.theilslopes.html#scipy.stats.theilslopes" title="scipy.stats.theilslopes" rel="nofollow">theilslopes</a>(y[,&nbsp;x,&nbsp;alpha])</td> 
 <td>Computes the Theil-Sen estimator for a set of points (x, y).</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.f_value.html#scipy.stats.f_value" title="scipy.stats.f_value" rel="nofollow">f_value</a>(*args,&nbsp;**kwds)</td> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.f_value.html#scipy.stats.f_value" title="scipy.stats.f_value" rel="nofollow">f_value</a> is deprecated!</td> 
 </tr> 
 </tbody> 
</table>

<table> 
 <tbody> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_1samp.html#scipy.stats.ttest_1samp" title="scipy.stats.ttest_1samp" rel="nofollow">ttest_1samp</a>(a,&nbsp;popmean[,&nbsp;axis,&nbsp;nan_policy])</td> 
 <td>Calculates the T-test for the mean of ONE group of scores.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_ind.html#scipy.stats.ttest_ind" title="scipy.stats.ttest_ind" rel="nofollow">ttest_ind</a>(a,&nbsp;b[,&nbsp;axis,&nbsp;equal_var,&nbsp;nan_policy])</td> 
 <td>Calculates the T-test for the means of two independent samples of scores.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_ind_from_stats.html#scipy.stats.ttest_ind_from_stats" title="scipy.stats.ttest_ind_from_stats" rel="nofollow">ttest_ind_from_stats</a>(mean1,&nbsp;std1,&nbsp;nobs1,&nbsp;...)</td> 
 <td>T-test for means of two independent samples from descriptive statistics.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_rel.html#scipy.stats.ttest_rel" title="scipy.stats.ttest_rel" rel="nofollow">ttest_rel</a>(a,&nbsp;b[,&nbsp;axis,&nbsp;nan_policy])</td> 
 <td>Calculates the T-test on TWO RELATED samples of scores, a and b.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kstest.html#scipy.stats.kstest" title="scipy.stats.kstest" rel="nofollow">kstest</a>(rvs,&nbsp;cdf[,&nbsp;args,&nbsp;N,&nbsp;alternative,&nbsp;mode])</td> 
 <td>Perform the Kolmogorov-Smirnov test for goodness of fit.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chisquare.html#scipy.stats.chisquare" title="scipy.stats.chisquare" rel="nofollow">chisquare</a>(f_obs[,&nbsp;f_exp,&nbsp;ddof,&nbsp;axis])</td> 
 <td>Calculates a one-way chi square test.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.power_divergence.html#scipy.stats.power_divergence" title="scipy.stats.power_divergence" rel="nofollow">power_divergence</a>(f_obs[,&nbsp;f_exp,&nbsp;ddof,&nbsp;axis,&nbsp;...])</td> 
 <td>Cressie-Read power divergence statistic and goodness of fit test.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ks_2samp.html#scipy.stats.ks_2samp" title="scipy.stats.ks_2samp" rel="nofollow">ks_2samp</a>(data1,&nbsp;data2)</td> 
 <td>Computes the Kolmogorov-Smirnov statistic on 2 samples.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.mannwhitneyu.html#scipy.stats.mannwhitneyu" title="scipy.stats.mannwhitneyu" rel="nofollow">mannwhitneyu</a>(x,&nbsp;y[,&nbsp;use_continuity,&nbsp;alternative])</td> 
 <td>Computes the Mann-Whitney rank test on samples x and y.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.tiecorrect.html#scipy.stats.tiecorrect" title="scipy.stats.tiecorrect" rel="nofollow">tiecorrect</a>(rankvals)</td> 
 <td>Tie correction factor for ties in the Mann-Whitney U and Kruskal-Wallis H tests.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rankdata.html#scipy.stats.rankdata" title="scipy.stats.rankdata" rel="nofollow">rankdata</a>(a[,&nbsp;method])</td> 
 <td>Assign ranks to data, dealing with ties appropriately.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ranksums.html#scipy.stats.ranksums" title="scipy.stats.ranksums" rel="nofollow">ranksums</a>(x,&nbsp;y)</td> 
 <td>Compute the Wilcoxon rank-sum statistic for two samples.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.wilcoxon.html#scipy.stats.wilcoxon" title="scipy.stats.wilcoxon" rel="nofollow">wilcoxon</a>(x[,&nbsp;y,&nbsp;zero_method,&nbsp;correction])</td> 
 <td>Calculate the Wilcoxon signed-rank test.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kruskal.html#scipy.stats.kruskal" title="scipy.stats.kruskal" rel="nofollow">kruskal</a>(*args,&nbsp;**kwargs)</td> 
 <td>Compute the Kruskal-Wallis H-test for independent samples</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.friedmanchisquare.html#scipy.stats.friedmanchisquare" title="scipy.stats.friedmanchisquare" rel="nofollow">friedmanchisquare</a>(*args)</td> 
 <td>Computes the Friedman test for repeated measurements</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.combine_pvalues.html#scipy.stats.combine_pvalues" title="scipy.stats.combine_pvalues" rel="nofollow">combine_pvalues</a>(pvalues[,&nbsp;method,&nbsp;weights])</td> 
 <td>Methods for combining the p-values of independent tests bearing upon the same hypothesis.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ss.html#scipy.stats.ss" title="scipy.stats.ss" rel="nofollow">ss</a>(*args,&nbsp;**kwds)</td> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ss.html#scipy.stats.ss" title="scipy.stats.ss" rel="nofollow">ss</a> is deprecated!</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.square_of_sums.html#scipy.stats.square_of_sums" title="scipy.stats.square_of_sums" rel="nofollow">square_of_sums</a>(*args,&nbsp;**kwds)</td> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.square_of_sums.html#scipy.stats.square_of_sums" title="scipy.stats.square_of_sums" rel="nofollow">square_of_sums</a> is deprecated!</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.jarque_bera.html#scipy.stats.jarque_bera" title="scipy.stats.jarque_bera" rel="nofollow">jarque_bera</a>(x)</td> 
 <td>Perform the Jarque-Bera goodness of fit test on sample data.</td> 
 </tr> 
 </tbody> 
</table>

<table> 
 <tbody> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ansari.html#scipy.stats.ansari" title="scipy.stats.ansari" rel="nofollow">ansari</a>(x,&nbsp;y)</td> 
 <td>Perform the Ansari-Bradley test for equal scale parameters</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.bartlett.html#scipy.stats.bartlett" title="scipy.stats.bartlett" rel="nofollow">bartlett</a>(*args)</td> 
 <td>Perform Bartlett’s test for equal variances</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.levene.html#scipy.stats.levene" title="scipy.stats.levene" rel="nofollow">levene</a>(*args,&nbsp;**kwds)</td> 
 <td>Perform Levene test for equal variances.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.shapiro.html#scipy.stats.shapiro" title="scipy.stats.shapiro" rel="nofollow">shapiro</a>(x[,&nbsp;a,&nbsp;reta])</td> 
 <td>Perform the Shapiro-Wilk test for normality.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.anderson.html#scipy.stats.anderson" title="scipy.stats.anderson" rel="nofollow">anderson</a>(x[,&nbsp;dist])</td> 
 <td>Anderson-Darling test for data coming from a particular distribution</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.anderson_ksamp.html#scipy.stats.anderson_ksamp" title="scipy.stats.anderson_ksamp" rel="nofollow">anderson_ksamp</a>(samples[,&nbsp;midrank])</td> 
 <td>The Anderson-Darling test for k-samples.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.binom_test.html#scipy.stats.binom_test" title="scipy.stats.binom_test" rel="nofollow">binom_test</a>(x[,&nbsp;n,&nbsp;p,&nbsp;alternative])</td> 
 <td>Perform a test that the probability of success is p.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.fligner.html#scipy.stats.fligner" title="scipy.stats.fligner" rel="nofollow">fligner</a>(*args,&nbsp;**kwds)</td> 
 <td>Perform Fligner-Killeen test for equality of variance.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.median_test.html#scipy.stats.median_test" title="scipy.stats.median_test" rel="nofollow">median_test</a>(*args,&nbsp;**kwds)</td> 
 <td>Mood’s median test.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.mood.html#scipy.stats.mood" title="scipy.stats.mood" rel="nofollow">mood</a>(x,&nbsp;y[,&nbsp;axis])</td> 
 <td>Perform Mood’s test for equal scale parameters.</td> 
 </tr> 
 </tbody> 
</table>

<table> 
 <tbody> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.boxcox.html#scipy.stats.boxcox" title="scipy.stats.boxcox" rel="nofollow">boxcox</a>(x[,&nbsp;lmbda,&nbsp;alpha])</td> 
 <td>Return a positive dataset transformed by a Box-Cox power transformation.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.boxcox_normmax.html#scipy.stats.boxcox_normmax" title="scipy.stats.boxcox_normmax" rel="nofollow">boxcox_normmax</a>(x[,&nbsp;brack,&nbsp;method])</td> 
 <td>Compute optimal Box-Cox transform parameter for input data.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.boxcox_llf.html#scipy.stats.boxcox_llf" title="scipy.stats.boxcox_llf" rel="nofollow">boxcox_llf</a>(lmb,&nbsp;data)</td> 
 <td>The boxcox log-likelihood function.</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.entropy.html#scipy.stats.entropy" title="scipy.stats.entropy" rel="nofollow">entropy</a>(pk[,&nbsp;qk,&nbsp;base])</td> 
 <td>Calculate the entropy of a distribution for given probability values.</td> 
 </tr> 
 </tbody> 
</table>

<table> 
 <tbody> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chisqprob.html#scipy.stats.chisqprob" title="scipy.stats.chisqprob" rel="nofollow">chisqprob</a>(*args,&nbsp;**kwds)</td> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chisqprob.html#scipy.stats.chisqprob" title="scipy.stats.chisqprob" rel="nofollow">chisqprob</a> is deprecated!</td> 
 </tr> 
 <tr> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.betai.html#scipy.stats.betai" title="scipy.stats.betai" rel="nofollow">betai</a>(*args,&nbsp;**kwds)</td> 
 <td><a href="http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.betai.html#scipy.stats.betai" title="scipy.stats.betai" rel="nofollow">betai</a> is deprecated!</td> 
 </tr> 
 </tbody> 
</table>

### describe函数 ###

这个函数的输出太难看了！

age = [23, 23, 27, 27, 39, 41, 47, 49, 50, 52, 54, 54, 56, 57, 58, 58, 60, 61]
    fat_percent = [9.5, 26.5, 7.8, 17.8, 31.4, 25.9, 27.4, 27.2, 31.2, 34.6, 42.5, 28.8, 33.4, 30.2, 34.1, 32.9, 41.2, 35.7]
    age = np.array(age)
    fat_percent = np.array(fat_percent)
    data = np.vstack([age, fat_percent]).reshape([-1, 2])
    
     print(stats.describe(data))

DescribeResult(nobs=18, minmax=(array(\[  7.8,  17.8\]), array(\[ 60.,  61.\])), mean=array(\[ 37.36111111,  37.86666667\]), variance=array(\[ 236.58604575,  188.78588235\]), skewness=array(\[-0.30733374,  0.40999364\]), kurtosis=array(\[-0.65245849, -1.26315357\]))

修改了一个输出结果形式

for key, value in stats.describe(data)._asdict().items():
        print(key, ':', value)

nobs : 18  
minmax : (array(\[  7.8,  17.8\]), array(\[ 60.,  61.\]))  
mean : \[ 37.36111111  37.86666667\]  
variance : \[ 236.58604575  188.78588235\]  
skewness : \[-0.30733374  0.40999364\]  
kurtosis : \[-0.65245849 -1.26315357\]

也可以使用pandas中的函数进行替代，这样输出比较舒服\[[python数据处理库pandas][python_pandas]\]

### 概率分布的熵和kl散度的计算 scipy.stats.entropy ###

scipy.stats.entropy(pk, qk=None, base=None)\[source\]  
    Calculate the entropy of a distribution for given probability values.  
    If only probabilities pk are given, the entropy is calculated as S = -sum(pk \* log(pk), axis=0).  
    If qk is not None, then compute the Kullback-Leibler divergence S = sum(pk \* log(pk / qk), axis=0).  
    This routine will normalize pk and qk if they don’t sum to 1.

**香农熵的计算entropy**

shannon_entropy = stats.entropy(ij/sum(ij), base=None)
    print(shannon_entropy)

**entropy的python直接实现**

shannon_entropy_func = lambda pij: -sum(pij*np.log(pij))
    shannon_entropy = shannon_entropy_func(ij[np.nonzero(ij)])
    print(shannon_entropy)

def entropy(counts):  
    '''Compute entropy.'''  
    ps = counts/float(sum(counts))  \# coerce to float and normalize  
    ps = ps\[nonzero(ps)\]            \# toss out zeros  
    H = -sum(ps \* numpy.log2(ps))   \# compute entropy

return H

**两个分布的kl散度的计算**

kl = sp.stats.entropy(fs_rv_dist, nonfs_rv_dist)

kl散度的其它实现\[[距离和相似度度量方法][Link 1]\]

\[scipy.stats.entropy[¶][Link 2]\]

### 假设检验相关的 ###

ttest\_1samp(a, popmean\[, axis\]) Calculates the T-test for the mean of ONE group of scores.  
ttest\_ind(a, b\[, axis, equal\_var\]) Calculates the T-test for the means of TWO INDEPENDENT samples of scores.  
ttest\_rel(a, b\[, axis\]) Calculates the T-test on TWO RELATED samples of scores, a and b.  
kstest(rvs, cdf\[, args, N, alternative, mode\]) Perform the Kolmogorov-Smirnov test for goodness of fit.  
chisquare(f\_obs\[, f\_exp, ddof, axis\]) Calculates a one-way chi square test.  
power\_divergence(f\_obs\[, f\_exp, ddof, axis, ...\]) Cressie-Read power divergence statistic and goodness of fit test.  
ks\_2samp(data1, data2) Computes the Kolmogorov-Smirnov statistic on 2 samples.  
mannwhitneyu(x, y\[, use\_continuity\]) Computes the Mann-Whitney rank test on samples x and y.  
tiecorrect(rankvals) Tie correction factor for ties in the Mann-Whitney U and Kruskal-Wallis H tests.  
rankdata(a\[, method\]) Assign ranks to data, dealing with ties appropriately.  
ranksums(x, y) Compute the Wilcoxon rank-sum statistic for two samples.  
wilcoxon(x\[, y, zero\_method, correction\]) Calculate the Wilcoxon signed-rank test.  
kruskal(\*args) Compute the Kruskal-Wallis H-test for independent samples  
friedmanchisquare(\*args) Computes the Friedman test for repeated measurements

ttest\_1samp实现了单样本t检验。因此，如果我们想检验数据Abra列的稻谷产量均值，通过零假设，这里我们假定总体稻谷产量均值为15000，我们有：

from scipy import stats as ss  
\# Perform one sample t-test using 1500 as the true mean  
print ss.ttest\_1samp(a = df.ix\[:, 'Abra'\], popmean = 15000)  
  
\# OUTPUT  
(-1.1281738488299586, 0.26270472069109496)

返回下述值组成的元祖：

*  t : 浮点或数组类型  
    t统计量
 *  prob : 浮点或数组类型  
    two-tailed p-value 双侧概率值

通过上面的输出，看到p值是0.267远大于α等于0.05，因此没有充分的证据说平均稻谷产量不是150000。将这个检验应用到所有的变量，同样假设均值为15000，我们有：

print ss.ttest\_1samp(a = df, popmean = 15000)  
  
\# OUTPUT  
(array(\[ -1.12817385,   1.07053437, -65.81425599,  -4.564575  ,   6.17156198\]),  
 array(\[  2.62704721e-01,   2.87680340e-01,   4.15643528e-70,  
          1.83764399e-05,   2.82461897e-08\]))

第一个数组是t统计量，第二个数组则是相应的p值。

[皮皮blog][blog]

### 列联表函数Contingency table functions    ###

chi2\_contingency(observed\[, correction, lambda\_\]) Chi-square test of independence of variables in a contingency table.  
contingency.expected\_freq(observed) Compute the expected frequencies from a contingency table.  
contingency.margins(a) Return a list of the marginal sums of the array a.  
fisher\_exact(table\[, alternative\]) Performs a Fisher exact test on a 2x2 contingency table.

### 绘图测试Plot-tests    ###

ppcc\_max(x\[, brack, dist\]) Returns the shape parameter that maximizes the probability plot correlation coefficient for ppcc\_plot(x, a, b\[, dist, plot, N\]) Returns (shape, ppcc), and optionally plots shape vs.  
probplot(x\[, sparams, dist, fit, plot\]) Calculate quantiles for a probability plot, and optionally show the plot.  
boxcox\_normplot(x, la, lb\[, plot, N\]) Compute parameters for a Box-Cox normality plot, optionally show it.

###  ###

### Statistical functions for masked arrays (scipy.stats.mstats) ###

蒙面统计函数Masked statistics functions

argstoarray(\*args) Constructs a 2D array from a group of sequences.  
betai(a, b, x) Returns the incomplete beta function.  
chisquare(f\_obs\[, f\_exp, ddof, axis\]) Calculates a one-way chi square test.  
count\_tied\_groups(x\[, use\_missing\]) Counts the number of tied values.  
describe(a\[, axis\]) Computes several descriptive statistics of the passed array.  
f\_oneway(\*args) Performs a 1-way ANOVA, returning an F-value and probability given any f\_value\_wilks\_lambda(ER, EF, dfnum, dfden, a, b) Calculation of Wilks lambda F-statistic for multivariate data, per Maxwell find\_repeats(arr) Find repeats in arr and return a tuple (repeats, repeat\_count).  
friedmanchisquare(\*args) Friedman Chi-Square is a non-parametric, one-way within-subjects ANOVA.  
kendalltau(x, y\[, use\_ties, use\_missing\]) Computes Kendall’s rank correlation tau on two variables x and y.  
kendalltau\_seasonal(x) Computes a multivariate Kendall’s rank correlation tau, for seasonal data.  
kruskalwallis(\*args) Compute the Kruskal-Wallis H-test for independent samples  
kruskalwallis(\*args) Compute the Kruskal-Wallis H-test for independent samples  
ks\_twosamp(data1, data2\[, alternative\]) Computes the Kolmogorov-Smirnov test on two samples.  
ks\_twosamp(data1, data2\[, alternative\]) Computes the Kolmogorov-Smirnov test on two samples.  
kurtosis(a\[, axis, fisher, bias\]) Computes the kurtosis (Fisher or Pearson) of a dataset.  
kurtosistest(a\[, axis\]) Tests whether a dataset has normal kurtosis  
linregress(\*args) Calculate a regression line  
mannwhitneyu(x, y\[, use\_continuity\]) Computes the Mann-Whitney statistic  
plotting\_positions(data\[, alpha, beta\]) Returns plotting positions (or empirical percentile points) for the data.  
mode(a\[, axis\]) Returns an array of the modal (most common) value in the passed array.  
moment(a\[, moment, axis\]) Calculates the nth moment about the mean for a sample.  
mquantiles(a\[, prob, alphap, betap, axis, limit\]) Computes empirical quantiles for a data array.

msign(x) Returns the sign of x, or 0 if x is masked.  
normaltest(a\[, axis\]) Tests whether a sample differs from a normal distribution.  
obrientransform(\*args) Computes a transform on input data (any number of columns).  
pearsonr(x, y) Calculates a Pearson correlation coefficient and the p-value for testing non-plotting\_positions(data\[, alpha, beta\]) Returns plotting positions (or empirical percentile points) for the data.  
pointbiserialr(x, y) Calculates a point biserial correlation coefficient and the associated p-value.  
rankdata(data\[, axis, use\_missing\]) Returns the rank (also known as order statistics) of each data point along scoreatpercentile(data, per\[, limit, ...\]) Calculate the score at the given ‘per’ percentile of the sequence a.  
sem(a\[, axis, ddof\]) Calculates the standard error of the mean (or standard error of measurement) signaltonoise(data\[, axis\]) Calculates the signal-to-noise ratio, as the ratio of the mean over standard skew(a\[, axis, bias\]) Computes the skewness of a data set.  
skewtest(a\[, axis\]) Tests whether the skew is different from the normal distribution.  
spearmanr(x, y\[, use\_ties\]) Calculates a Spearman rank-order correlation coefficient and the p-value theilslopes(y\[, x, alpha\]) Computes the Theil slope as the median of all slopes between paired values.  
threshold(a\[, threshmin, threshmax, newval\]) Clip array to a given value.  
tmax(a, upperlimit\[, axis, inclusive\]) Compute the trimmed maximum  
tmean(a\[, limits, inclusive\]) Compute the trimmed mean.  
tmin(a\[, lowerlimit, axis, inclusive\]) Compute the trimmed minimum  
trim(a\[, limits, inclusive, relative, axis\]) Trims an array by masking the data outside some given limits.  
trima(a\[, limits, inclusive\]) Trims an array by masking the data outside some given limits.  
trimboth(data\[, proportiontocut, inclusive, ...\]) Trims the smallest and largest data values.  
trimmed\_stde(a\[, limits, inclusive, axis\]) Returns the standard error of the trimmed mean along the given axis.  
trimr(a\[, limits, inclusive, axis\]) Trims an array by masking some proportion of the data on each end.  
trimtail(data\[, proportiontocut, tail, ...\]) Trims the data by masking values from one tail.  
tsem(a\[, limits, inclusive\]) Compute the trimmed standard error of the mean.  
ttest\_onesamp(a, popmean\[, axis\]) Calculates the T-test for the mean of ONE group of scores.  
ttest\_ind(a, b\[, axis\]) Calculates the T-test for the means of TWO INDEPENDENT samples of ttest\_onesamp(a, popmean\[, axis\]) Calculates the T-test for the mean of ONE group of scores.  
ttest\_rel(a, b\[, axis\]) Calculates the T-test on TWO RELATED samples of scores, a and b.  
tvar(a\[, limits, inclusive\]) Compute the trimmed variance  
variation(a\[, axis\]) Computes the coefficient of variation, the ratio of the biased standard deviation winsorize(a\[, limits, inclusive, inplace, axis\]) Returns a Winsorized version of the input array.  
zmap(scores, compare\[, axis, ddof\]) Calculates the relative z-scores.  
zscore(a\[, axis, ddof\]) Calculates the z score of each value in the sample, relative to the sample

### 单变量和多变量核密度估计Univariate and multivariate kernel density estimation (scipy.stats.kde)    ###

gaussian\_kde(dataset\[, bw\_method\]) Representation of a kernel-density estimate using Gaussian kernels.[  
][blog]

[皮皮blog][blog]

# 统计函数使用举例 #

## 连续分布-Norm高斯分布 ##

\{高斯\[正态\]分布随机变量,A normal continuous random variable.\}

### **生成服从高斯分布的随机向量（从正态分布中采样）stats.norm.rvs(loc, scale, size)** ###

参数：

The location (loc) keyword specifies the mean.

The scale (scale) keyword specifies the standard deviation.

norm通过loc和scale参数可以指定随机变量的偏移和缩放参数。 对于正态分布的随机变量来说，这两个参数相当于指定其期望值和标准差。

高斯分布N(0,0.01)随机偏差
    y = stats.norm.rvs(loc=0, scale=0.1, size=10)

输出：array([ 0.05419826,  0.04151471, -0.10784729,  0.18283546,  0.02348312, -0.04611974,  0.0069336 ,  0.03840133, -0.05015316,  0.23315205])

y.stats()  
(array(0.0), array(0.1)

**Note**: 也可以使用numpy.random.norm函数生成高斯分布随机数\[[numpy库 - 随机数模块numpy.random][numpy_ - _numpy.random]\]。

### 求正态分布最佳拟合参数stats.norm.fit(x) ###

>>> X =stats.norm(loc=1.0,scale=2.0,size = 100)  
可以使用fit()方法对随机取样序列x进行拟合，返回的是与随机取样值最吻合的随机变量的参数  
>>> stats.norm.fit(x) \#得到随机序列的期望值和标准差  
array(\[ 1.01810091,2.00046946\])

**求正态分布N(1,1)概率密度函数某个x对应的值**

lambda x: norm.pdf(x, 1, 1)

Note: 从正态分布概率密度中看出，这个和norm.pdf(x - 1)是不一样的，只有标准差为1时才相等。

**求正态分布N(1,1)累积分布函数某个x对应的值**

lambda x: norm.cdf(x, 1, 1)

### 绘制一维和二维正态分布概率密度图 ###

\[ [概率论：高斯分布][Link 3]\]

\[[scipy.stats.norm][]\]

## 均匀分布 ##

mu = uniform.rvs(size=N)  # 从均匀分布采样

## 伽玛分布 ##

伽玛分布需要额外的形状参数。伽玛分布可用于描述等待k个独立的随机事件发生所需的时间，k就是伽玛分布的形状参数。  
伽玛分布的尺度参数theta和随机事件发生的频率相关，由scale参数指定。  
>>> stats.gamma.stats(2.0,scale=2)   
(array(4.0), array(8.0))  
根据伽玛分布的数学定义可知其期望值为k\*theta,方差为k\*theta^2 。上面的程序验证了这两个公式。 当随机分布有额外的形状参数时，它所对应的rvs()、pdf()等方法都会增加额外的参数以接收形状参数。

## 离散分布-二项分布 ##

假设有一种只有两个结果的试验，其成功概率为 P,那么二项分布描述了进行n次这样的独立试验而成功k次的概率。  
二项分布的概率质量函数公式如下：

![Center][]

使用二项分布的概率质量函数pmf()可以很容易计算出现k次6点的概率。

#### **pmf()** ####

pmf()的第一个参数为随机变量的取值，后面的参数为描述随机分布所需的参数。对于二项分布来说，参数分别为n和P,而取值范围则为0到n之间的整数。

程序通过二项分布的概率质量公式计算投掷5次骰子出现0到6所对应的概率：

>>> stats.binom.pmf(range(6), 5, 1/6.0)  
array(\[0.401878, 0.401878, 0.166751, 0.032150, 0.003215, 0.000129\])

由结果可知：出现0或1次6点的概率为40.2%,而出现3次6点的概率为3.215%

### 泊松分布 ###

在二项分布中，如果试验次数n很大，而每次试验成功的概率p很小，其乘积np比较适中，那么试验成功次数的概率可以用泊松分布近似描述。  
在泊松分布中，使用lambda描述单位时间(或单位面积)内随机事件的平均发生率。如果将二项分布中的试验次数n看作单位时间内所做的试验次数，那么它和事件出现概率P的乘积就是事件的平均发生率，即lambda = np。  
泊松分布的概率质量函数公式如下：  
![Center 1][]

#### 二项分布的近似分布 ####

程序分别计算二项分布和泊松分布的概率质量函数，当n足够大时，二者是十分接近的。  
程序中事件平均发生率lambda恒等于10。根据二项分布的试验次数计算每次事件出现的概率p=lambda/n。  
>>> \_lambda = 10.0   
>>> k = np.arange(20)  
>>> possion = stats .poisson .pmf(k, \_lambda) \# 泊松分布   
>>> binom100 = stats.binom.pmf(k, 100, \_lambda/100) \#二项式分布 100  
>>> binom1000=stats.binom.pmf(k, 1000 , \_lambda/1000) \#二项式分布 1000  
>>> np.max(np.abs(binom100-possion)) \# 计算最大误差  
 0.006755311103353312  
>>> np.max(np.abs(binom1000-possion))\# n为 1000时，误差较小  
0.00063017540509099912  
![Center 2][]

#### 泊松分布的模拟过程 ####

泊松分布适合描述单位时间内随机事件发生次数的分布情况。例如某设施在一定时间内的 使用次数。机器出现故障的次数。自然灾害发生的次数等等。

下面使用随机数模拟泊松分布，并与其概率质量函数进行比较，事件每秒的平均发生次数为lambda=10。其中观察时间分别为1000秒，50000秒。可以看出：观察时间越长，事件每秒发生的次数就越符合泊松分布。

>>> \_lambda = 10  
>>> time = 10000  
>>> t = np.random.rand(\_lambda\*time )\*time  
>>> count, time\_edges = np.histogram(t, bins=time, range=(0,time))  
>>> count  
array(\[10, 9, 8, …, 11, 10, 18\])  
>>>x = count\_edges\[:-1\]   
>>> dist, count\_edges = np. histogram (count, bins=20, range= (0,20), normed=True)  
>>> poisson = stats .poisson.pmf(x, \_lambda)  
>>> np.max(np.abs(dist-poisson)) \#最大误差很小,符合泊松分布  
 0.0088356241037075706

![Center 3][]

**Note**: 用rand()产生平均分布于0到time之间的\_lambda\*time 个事件所发生的时刻。  
用histogram()可以统计数组t中每秒之内事件发生的次数count。  
根据泊松分布的定义，count数组中数值的分布情况应该符合泊松分布。统计事件次数在0到20区间内的概率分布。当histogram()的normed参数为True并且每个统计区间的长度为1时，其结果和概率质量函数相等。

#### 泊松分布的时间间隔:[伽玛分布][Link 4] ####

还可以换一个角度看随机事件的分布问题。可以观察相邻两个事件之间时间间隔的分布情况，或者隔k个事件的时间间隔的分布情况。根据概率论，事件之间的时间间隔应符合伽玛分布，由于时间间隔可以是任意数值，因此伽玛分布是一种连续概率分布。伽玛分布的概率密度函数公式如下，它描述第k个亊件发生所需的等待时间的概率分布。伽玛函数，当 k为整数时，它的值和k的阶乘k!相等。  
  
![Center 4][]

程序模拟事件的时间间隔的伽玛分布，观察时间为1 000秒，平均每秒产生10个事件。  
图中“k=1”，它表示相邻两个事件之间的时间间 隔的分布，而“k=2”则表示相隔一个事件的两个事件之间的时间间隔的分布，可以看出它们都符合伽玛分布.

![Center 5][]

>>> \_lambda = 10  
>>> time = 10000  
>>> t = np.random.rand(\_lambda\*time)\*time  
>>> t.sort()\#计算事性前后的时间间隔，需要先对随机时刻进行排序  
>>> s1 = t\[1:\] - t\[:-1\] \#相邻两个事件之间的时间间隔   
>>> s2 = t\[2:\] - t\[:-2\] \#相隔一个事件的两个亊件之间的时间间隔  
>>> dist1, x1= np.histogram(s1, bins=100, normed=True)  
>>> dist2, x2 = np.histogram(s2 , bins=100, normed=True)  
>>> gamma1 = stats.gamma.pdf((x1\[:-1\]+x1\[1:\])/2, 1, scale=1.0/\_lambda)  
>>> gamma2 = stats.gamma.pdf((x2\[:-1\]+x2\[1:\])/2, 2, scale=1.0/\_lambda)  
>>> np.max(np.abs(gamma1 - dist1))  
0.13557317865888141  
>>> np.max(np.abs(gamma2 - dist2))  
0.087375030861794656  
>>> np.max(gamma1), np.max(gamma2)  
(9.3483221580498537, 3.6767953241013656)\#由于概率密度函数的值本身比较大，因此上面的误差已经很小了:  
Note:模拟伽玛分布:  
首先在10000秒之内产生100000个随机事件发生的时刻.因此事件的平均发生次数为每秒10次;  
为了计算事性前后的时间间隔，需要先对随机时刻进行排序;  
histogram()返回的第二个值为统计区间的边界，采用gamma.pdf()计算伽玛分布的概率密度时，使用各个区间的中值进行计算。Pdf()的第二个参数为k值，scale参数为1/λ;

from:[http://blog.csdn.net/pipisorry/article/details/49515215][blog.csdn.net_pipisorry_article_details_49515215]

ref:Statistical functions ([scipy.stats][])

[python标准库中的随机分布函数][python]

[blog.csdn.net_pipisorry_article_details_49515215]: http://blog.csdn.net/pipisorry/article/details/49515215
[rv_continuous]: http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.html#scipy.stats.rv_continuous
[rv_discrete]: http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.html#scipy.stats.rv_discrete
[blog]: http://blog.csdn.net/pipisorry
[Continuous distributions]: http://docs.scipy.org/doc/scipy/reference/stats.html#continuous-distributions
[Examples]: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_discrete.html#scipy.stats.rv_discrete
[python_pandas]: http://blog.csdn.net/pipisorry/article/details/18012125
[Link 1]: http://blog.csdn.net/pipisorry/article/details/45651315
[Link 2]: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.entropy.html#scipy-stats-entropy
[numpy_ - _numpy.random]: http://blog.csdn.net/pipisorry/article/details/39508417
[Link 3]: http://blog.csdn.net/pipisorry/article/details/49516209
[scipy.stats.norm]: http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy-stats-norm
[Center]: /images/20220731/1173953ff6724f29b2f1555f17db6a0d.png
[Center 1]: /images/20220731/969df6950d784ed98305b05b094072fd.png
[Center 2]: /images/20220731/a0fdebd80b894e7dbf1f175eb12d1bf2.png
[Center 3]: /images/20220731/3f009f71fbb94fb2a9bf792f0be6ef00.png
[Link 4]: https://zh.wikipedia.org/zh-hans/%E4%BC%BD%E7%8E%9B%E5%88%86%E5%B8%83
[Center 4]: /images/20220731/866f4d0eda864776ac8d10616bed6e37.png
[Center 5]: /images/20220731/bb531129896043948194ed786507ac76.png
[scipy.stats]: http://docs.scipy.org/doc/scipy/reference/stats.html#module-scipy.stats
[python]: http://ju.outofmemory.cn/entry/51762