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<!doctype html>
<html lang="en">
<head>
<meta charset="UTF-8">
<title>Distributions - jStat Documentation</title>
<link rel="stylesheet" href="assets/style.css" />
<link rel="stylesheet" href="assets/sh.css" />
</head>
<body>
<div id="container">
<header>
<h1>jStat v1.9.3 Documentation</h1>
<div id="gtoc">
<p><a href="index.html">Index</a> | <a href="all.html">View on single page</a></p>
</div>
<hr />
</header>
<div id="toc"><h2>Table Of Contents</h2><ul><li><a href="#distributions">Distributions</a><ul><li><a href="#jStat.beta">jStat.beta( alpha, beta )</a><ul><li><a href="#jStat.beta.pdf">jStat.beta.pdf( x, alpha, beta )</a></li><li><a href="#jStat.beta.cdf">jStat.beta.cdf( x, alpha, beta )</a></li><li><a href="#jStat.beta.inv">jStat.beta.inv( p, alpha, beta )</a></li><li><a href="#jStat.beta.mean">jStat.beta.mean( alpha, beta )</a></li><li><a href="#jStat.beta.median">jStat.beta.median( alpha, beta )</a></li><li><a href="#jStat.beta.mode">jStat.beta.mode( alpha, beta )</a></li><li><a href="#jStat.beta.sample">jStat.beta.sample( alpha, beta )</a></li><li><a href="#jStat.beta.variance">jStat.beta.variance( alpha, beta )</a></li></ul></li><li><a href="#jStat.centralF">jStat.centralF( df1, df2 )</a><ul><li><a href="#jStat.centralF.pdf">jStat.centralF.pdf( x, df1, df2 )</a></li><li><a href="#jStat.centralF.cdf">jStat.centralF.cdf( x, df1, df2 )</a></li><li><a href="#jStat.centralF.inv">jStat.centralF.inv( p, df1, df2 )</a></li><li><a href="#jStat.centralF.mean">jStat.centralF.mean( df1, df2 )</a></li><li><a href="#jStat.centralF.mode">jStat.centralF.mode( df1, df2 )</a></li><li><a href="#jStat.centralF.sample">jStat.centralF.sample( df1, df2 )</a></li><li><a href="#jStat.centralF.variance">jStat.centralF.variance( df1, df2 )</a></li></ul></li><li><a href="#jStat.cauchy">jStat.cauchy( local, scale )</a><ul><li><a href="#jStat.cauchy.pdf">jStat.cauchy.pdf( x, local, scale )</a></li><li><a href="#jStat.cauchy.cdf">jStat.cauchy.cdf( x, local, scale )</a></li><li><a href="#jStat.cauchy.inv">jStat.cauchy.inv( p, local, scale )</a></li><li><a href="#jStat.cauchy.median">jStat.cauchy.median( local, scale )</a></li><li><a href="#jStat.cauchy.mode">jStat.cauchy.mode( local, scale )</a></li><li><a href="#jStat.cauchy.sample">jStat.cauchy.sample( local, scale )</a></li><li><a href="#jStat.cauchy.variance">jStat.cauchy.variance( local, scale )</a></li></ul></li><li><a href="#jStat.chisquare">jStat.chisquare( dof )</a><ul><li><a href="#jStat.chisquare.pdf">jStat.chisquare.pdf( x, dof )</a></li><li><a href="#jStat.chisquare.cdf">jStat.chisquare.cdf( x, dof )</a></li><li><a href="#jStat.chisquare.inv">jStat.chisquare.inv( p, dof )</a></li><li><a href="#jStat.chisquare.mean">jStat.chisquare.mean( dof )</a></li><li><a href="#jStat.chisquare.median">jStat.chisquare.median( dof )</a></li><li><a href="#jStat.chisquare.mode">jStat.chisquare.mode( dof )</a></li><li><a href="#jStat.chisquare.sample">jStat.chisquare.sample( dof )</a></li><li><a href="#jStat.chisquare.variance">jStat.chisquare.variance( dof )</a></li></ul></li><li><a href="#jStat.exponential">jStat.exponential( rate )</a><ul><li><a href="#jStat.exponential.pdf">jStat.exponential.pdf( x, rate )</a></li><li><a href="#jStat.exponential.cdf">jStat.exponential.cdf( x, rate )</a></li><li><a href="#jStat.exponential.inv">jStat.exponential.inv( p, rate )</a></li><li><a href="#jStat.exponential.mean">jStat.exponential.mean( rate )</a></li><li><a href="#jStat.exponential.median">jStat.exponential.median( rate )</a></li><li><a href="#jStat.exponential.mode">jStat.exponential.mode( rate )</a></li><li><a href="#jStat.exponential.sample">jStat.exponential.sample( rate )</a></li><li><a href="#jStat.exponential.variance">jStat.exponential.variance( rate )</a></li></ul></li><li><a href="#jStat.gamma">jStat.gamma( shape, scale )</a><ul><li><a href="#jStat.gamma.pdf">jStat.gamma.pdf( x, shape, scale )</a></li><li><a href="#jStat.gamma.cdf">jStat.gamma.cdf( x, shape, scale )</a></li><li><a href="#jStat.gamma.inv">jStat.gamma.inv( p, shape, scale )</a></li><li><a href="#jStat.gamma.mean">jStat.gamma.mean( shape, scale )</a></li><li><a href="#jStat.gamma.mode">jStat.gamma.mode( shape, scale )</a></li><li><a href="#jStat.gamma.sample">jStat.gamma.sample( shape, scale )</a></li><li><a href="#jStat.gamma.variance">jStat.gamma.variance( shape, scale )</a></li></ul></li><li><a href="#jStat.invgamma">jStat.invgamma( shape, scale )</a><ul><li><a href="#jStat.invgamma.pdf">jStat.invgamma.pdf( x, shape, scale )</a></li><li><a href="#jStat.invgamma.cdf">jStat.invgamma.cdf( x, shape, scale )</a></li><li><a href="#jStat.invgamma.inv">jStat.invgamma.inv( p, shape, scale )</a></li><li><a href="#jStat.invgamma.mean">jStat.invgamma.mean( shape, scale )</a></li><li><a href="#jStat.invgamma.mode">jStat.invgamma.mode( shape, scale )</a></li><li><a href="#jStat.invgamma.sample">jStat.invgamma.sample( shape, scale )</a></li><li><a href="#jStat.invgamma.variance">jStat.invgamma.variance( shape, scale )</a></li></ul></li><li><a href="#jStat.kumaraswamy">jStat.kumaraswamy( alpha, beta )</a><ul><li><a href="#jStat.kumaraswamy.pdf">jStat.kumaraswamy.pdf( x, a, b )</a></li><li><a href="#jStat.kumaraswamy.cdf">jStat.kumaraswamy.cdf( x, alpha, beta )</a></li><li><a href="#jStat.kumaraswamy.inv">jStat.kumaraswamy.inv( p, alpha, beta )</a></li><li><a href="#jStat.kumaraswamy.mean">jStat.kumaraswamy.mean( alpha, beta )</a></li><li><a href="#jStat.kumaraswamy.median">jStat.kumaraswamy.median( alpha, beta )</a></li><li><a href="#jStat.kumaraswamy.mode">jStat.kumaraswamy.mode( alpha, beta )</a></li><li><a href="#jStat.kumaraswamy.variance">jStat.kumaraswamy.variance( alpha, beta )</a></li></ul></li><li><a href="#jStat.lognormal">jStat.lognormal( mu, sigma )</a><ul><li><a href="#jStat.lognormal.pdf">jStat.lognormal.pdf( x, mu, sigma )</a></li><li><a href="#jStat.lognormal.cdf">jStat.lognormal.cdf( x, mu, sigma )</a></li><li><a href="#jStat.lognormal.inv">jStat.lognormal.inv( p, mu, sigma )</a></li><li><a href="#jStat.lognormal.mean">jStat.lognormal.mean( mu, sigma )</a></li><li><a href="#jStat.lognormal.median">jStat.lognormal.median( mu, sigma )</a></li><li><a href="#jStat.lognormal.mode">jStat.lognormal.mode( mu, sigma )</a></li><li><a href="#jStat.lognormal.sample">jStat.lognormal.sample( mu, sigma )</a></li><li><a href="#jStat.lognormal.variance">jStat.lognormal.variance( mu, sigma )</a></li></ul></li><li><a href="#jStat.normal">jStat.normal( mean, std )</a><ul><li><a href="#jStat.normal.pdf">jStat.normal.pdf( x, mean, std )</a></li><li><a href="#jStat.normal.cdf">jStat.normal.cdf( x, mean, std )</a></li><li><a href="#jStat.normal.inv">jStat.normal.inv( p, mean, std )</a></li><li><a href="#jStat.normal.mean">jStat.normal.mean( mean, std )</a></li><li><a href="#jStat.normal.median">jStat.normal.median( mean, std )</a></li><li><a href="#jStat.normal.mode">jStat.normal.mode( mean, std )</a></li><li><a href="#jStat.normal.sample">jStat.normal.sample( mean, std )</a></li><li><a href="#jStat.normal.variance">jStat.normal.variance( mean, std )</a></li></ul></li><li><a href="#jStat.pareto">jStat.pareto( scale, shape )</a><ul><li><a href="#jStat.pareto.pdf">jStat.pareto.pdf( x, scale, shape )</a></li><li><a href="#jStat.pareto.inv">jStat.pareto.inv( p, scale, shape )</a></li><li><a href="#jStat.pareto.cdf">jStat.pareto.cdf( x, scale, shape )</a></li><li><a href="#jStat.pareto.mean">jStat.pareto.mean( scale, shape )</a></li><li><a href="#jStat.pareto.median">jStat.pareto.median( scale, shape )</a></li><li><a href="#jStat.pareto.mode">jStat.pareto.mode( scale, shape )</a></li><li><a href="#jStat.pareto.variance">jStat.pareto.variance( scale, shape )</a></li></ul></li><li><a href="#jStat.studentt">jStat.studentt( dof )</a><ul><li><a href="#jStat.studentt.pdf">jStat.studentt.pdf( x, dof )</a></li><li><a href="#jStat.studentt.cdf">jStat.studentt.cdf( x, dof )</a></li><li><a href="#jStat.studentt.inv">jStat.studentt.inv( p, dof )</a></li><li><a href="#jStat.studentt.mean">jStat.studentt.mean( dof )</a></li><li><a href="#jStat.studentt.median">jStat.studentt.median( dof )</a></li><li><a href="#jStat.studentt.mode">jStat.studentt.mode( dof )</a></li><li><a href="#jStat.studentt.sample">jStat.studentt.sample( dof )</a></li><li><a href="#jStat.studentt.variance">jStat.studentt.variance( dof )</a></li></ul></li><li><a href="#jStat.tukey">jStat.tukey( nmeans, dof )</a><ul><li><a href="#jStat.tukey.cdf">jStat.tukey.cdf( q, nmeans, dof )</a></li><li><a href="#jStat.tukey.inv">jStat.tukey.inv( p, nmeans, dof )</a></li></ul></li><li><a href="#jStat.weibull">jStat.weibull( scale, shape )</a><ul><li><a href="#jStat.weibull.pdf">jStat.weibull.pdf( x, scale, shape )</a></li><li><a href="#jStat.weibull.cdf">jStat.weibull.cdf( x, scale, shape )</a></li><li><a href="#jStat.weibull.inv">jStat.weibull.inv( p, scale, shape )</a></li><li><a href="#jStat.weibull.mean">jStat.weibull.mean( scale, shape )</a></li><li><a href="#jStat.weibull.median">jStat.weibull.median( scale, shape )</a></li><li><a href="#jStat.weibull.mode">jStat.weibull.mode( scale, shape )</a></li><li><a href="#jStat.weibull.sample">jStat.weibull.sample( scale, shape )</a></li><li><a href="#jStat.weibull.variance">jStat.weibull.variance( scale, shape )</a></li></ul></li><li><a href="#jStat.uniform">jStat.uniform( a, b )</a><ul><li><a href="#jStat.uniform.pdf">jStat.uniform.pdf( x, a, b )</a></li><li><a href="#jStat.uniform.cdf">jStat.uniform.cdf( x, a, b )</a></li><li><a href="#jStat.uniform.inv">jStat.uniform.inv( p, a, b)</a></li><li><a href="#jStat.uniform.mean">jStat.uniform.mean( a, b )</a></li><li><a href="#jStat.uniform.median">jStat.uniform.median( a, b )</a></li><li><a href="#jStat.uniform.mode">jStat.uniform.mode( a, b )</a></li><li><a href="#jStat.uniform.sample">jStat.uniform.sample( a, b )</a></li><li><a href="#jStat.uniform.variance">jStat.uniform.variance( a, b )</a></li></ul></li><li><a href="#jStat.binomial">jStat.binomial</a><ul><li><a href="#jStat.binomial.pdf">jStat.binomial.pdf( k, n, p )</a></li><li><a href="#jStat.binomial.cdf">jStat.binomial.cdf( k, n, p )</a></li></ul></li><li><a href="#jStat.negbin">jStat.negbin</a><ul><li><a href="#jStat.negbin.pdf">jStat.negbin.pdf( k, r, p )</a></li><li><a href="#jStat.negbin.cdf">jStat.negbin.cdf( x, r, p )</a></li></ul></li><li><a href="#jStat.hypgeom">jStat.hypgeom</a><ul><li><a href="#jStat.hypgeom.pdf">jStat.hypgeom.pdf( k, N, m, n )</a></li><li><a href="#jStat.hypgeom.cdf">jStat.hypgeom.cdf( x, N, m, n )</a></li></ul></li><li><a href="#jStat.poisson">jStat.poisson</a><ul><li><a href="#jStat.poisson.pdf">jStat.poisson.pdf( k, l )</a></li><li><a href="#jStat.poisson.cdf">jStat.poisson.cdf( x, l )</a></li><li><a href="#jStat.poisson.sample">jStat.poisson.sample( l )</a></li></ul></li><li><a href="#jStat.triangular">jStat.triangular</a><ul><li><a href="#jStat.triangular.pdf">jStat.triangular.pdf( x, a, b, c )</a></li><li><a href="#jStat.triangular.cdf">jStat.triangular.cdf( x, a, b, c )</a></li><li><a href="#jStat.triangular.mean">jStat.triangular.mean( a, b, c )</a></li><li><a href="#jStat.triangular.median">jStat.triangular.median( a, b, c )</a></li><li><a href="#jStat.triangular.mode">jStat.triangular.mode( a, b, c )</a></li><li><a href="#jStat.triangular.sample">jStat.triangular.sample( a, b, c )</a></li><li><a href="#jStat.triangular.variance">jStat.triangular.variance( a, b, c )</a></li></ul></li><li><a href="#jStat.arcsine">jStat.arcsine( a, b )</a><ul><li><a href="#jStat.arcsine.pdf">jStat.arcsine.pdf( x, a, b )</a></li><li><a href="#jStat.arcsine.cdf">jStat.arcsine.cdf( x, a, b )</a></li><li><a href="#jStat.arcsine.inv">jStat.arcsine.inv(p, a, b)</a></li><li><a href="#jStat.arcsine.mean">jStat.arcsine.mean( a, b )</a></li><li><a href="#jStat.arcsine.median">jStat.arcsine.median( a, b )</a></li><li><a href="#jStat.arcsine.mode">jStat.arcsine.mode( a, b )</a></li><li><a href="#jStat.arcsine.sample">jStat.arcsine.sample( a, b )</a></li><li><a href="#jStat.arcsine.variance">jStat.arcsine.variance( a, b )</a></li></ul></li></ul></li></ul><hr /></div>
<h2 id="distributions">Distributions</h2>
<h3 id="jStat.beta">jStat.beta( alpha, beta )</h3>
<h4 id="jStat.beta.pdf">jStat.beta.pdf( x, alpha, beta )</h4>
<p>Returns the value of <code>x</code> in the Beta distribution with parameters <code>alpha</code> and <code>beta</code>.</p>
<h4 id="jStat.beta.cdf">jStat.beta.cdf( x, alpha, beta )</h4>
<p>Returns the value of <code>x</code> in the cdf for the Beta distribution with parameters <code>alpha</code> and <code>beta</code>.</p>
<h4 id="jStat.beta.inv">jStat.beta.inv( p, alpha, beta )</h4>
<p>Returns the value of <code>p</code> in the inverse of the cdf for the Beta distribution with parameters <code>alpha</code> and <code>beta</code>.</p>
<h4 id="jStat.beta.mean">jStat.beta.mean( alpha, beta )</h4>
<p>Returns the mean of the Beta distribution with parameters <code>alpha</code> and <code>beta</code>.</p>
<h4 id="jStat.beta.median">jStat.beta.median( alpha, beta )</h4>
<p>Returns the median of the Beta distribution with parameters <code>alpha</code> and <code>beta</code>.</p>
<h4 id="jStat.beta.mode">jStat.beta.mode( alpha, beta )</h4>
<p>Returns the mode of the Beta distribution with parameters <code>alpha</code> and <code>beta</code>.</p>
<h4 id="jStat.beta.sample">jStat.beta.sample( alpha, beta )</h4>
<p>Returns a random number whose distribution is the Beta distribution with parameters <code>alpha</code> and <code>beta</code>.</p>
<h4 id="jStat.beta.variance">jStat.beta.variance( alpha, beta )</h4>
<p>Returns the variance of the Beta distribution with parameters <code>alpha</code> and <code>beta</code>.</p>
<h3 id="jStat.centralF">jStat.centralF( df1, df2 )</h3>
<p>The F Distrbution is used frequently in analyses of variance. The distribution is parameterized by two degrees of freedom (<code>df1</code> and <code>df2</code>). It is defined continuously on x in [0, infinity).</p>
<p>In all cases, <code>df1</code> is the "numerator degrees of freedom" and <code>df2</code> is the "denominator degrees of freedom", which parameterize the distribtuion.</p>
<h4 id="jStat.centralF.pdf">jStat.centralF.pdf( x, df1, df2 )</h4>
<p>Given <code>x</code> in the range [0, infinity), returns the probability density of the (central) F distribution at <code>x</code>.</p>
<p>This function corresponds to the <code>df(x, df1, df2)</code> function in R.</p>
<h4 id="jStat.centralF.cdf">jStat.centralF.cdf( x, df1, df2 )</h4>
<p>Given x in the range [0, infinity), returns the cumulative probability density of the central F distribution. That is, <code>jStat.centralF.cdf(2.5, 10, 20)</code> will return the probability that a number randomly selected from the central F distribution with <code>df1 = 10</code> and <code>df2 = 20</code> will be less than 2.5.</p>
<p>This function corresponds to the <code>pf(q, df1, df2)</code> function in R.</p>
<h4 id="jStat.centralF.inv">jStat.centralF.inv( p, df1, df2 )</h4>
<p>Given <code>p</code> in [0, 1), returns the value of x for which the cumulative probability density of the central F distribution is p. That is, <code>jStat.centralF.inv(p, df1, df2) = x</code> if and only if <code>jStat.centralF.inv(x, df1, df2) = p</code>.</p>
<p>This function corresponds to the <code>qf(p, df1, df2)</code> function in R.</p>
<h4 id="jStat.centralF.mean">jStat.centralF.mean( df1, df2 )</h4>
<p>Returns the mean of the (Central) F distribution.</p>
<h4 id="jStat.centralF.mode">jStat.centralF.mode( df1, df2 )</h4>
<p>Returns the mode of the (Central) F distribution.</p>
<h4 id="jStat.centralF.sample">jStat.centralF.sample( df1, df2 )</h4>
<p>Returns a random number whose distribution is the (Central) F distribution.</p>
<p>This function corresponds to the <code>rf(n, df1, df2)</code> function in R.</p>
<h4 id="jStat.centralF.variance">jStat.centralF.variance( df1, df2 )</h4>
<p>Returns the variance of the (Central) F distribution.</p>
<h3 id="jStat.cauchy">jStat.cauchy( local, scale )</h3>
<h4 id="jStat.cauchy.pdf">jStat.cauchy.pdf( x, local, scale )</h4>
<p>Returns the value of <code>x</code> in the pdf of the Cauchy distribution with a location (median) of <code>local</code> and scale factor of <code>scale</code>.</p>
<h4 id="jStat.cauchy.cdf">jStat.cauchy.cdf( x, local, scale )</h4>
<p>Returns the value of <code>x</code> in the cdf of the Cauchy distribution with a location (median) of <code>local</code> and scale factor of <code>scale</code>.</p>
<h4 id="jStat.cauchy.inv">jStat.cauchy.inv( p, local, scale )</h4>
<p>Returns the value of <code>p</code> in the inverse of the cdf for the Cauchy distribution with a location (median) of <code>local</code> and scale factor of <code>scale</code>.</p>
<h4 id="jStat.cauchy.median">jStat.cauchy.median( local, scale )</h4>
<p>Returns the value of the median for the Cauchy distribution with a location (median) of <code>local</code> and scale factor of <code>scale</code>.</p>
<h4 id="jStat.cauchy.mode">jStat.cauchy.mode( local, scale )</h4>
<p>Returns the value of the mode for the Cauchy distribution with a location (median) of <code>local</code> and scale factor of <code>scale</code>.</p>
<h4 id="jStat.cauchy.sample">jStat.cauchy.sample( local, scale )</h4>
<p>Returns a random number whose distribution is the Cauchy distribution with a location (median) of <code>local</code> and scale factor of <code>scale</code>.</p>
<h4 id="jStat.cauchy.variance">jStat.cauchy.variance( local, scale )</h4>
<p>Returns the value of the variance for the Cauchy distribution with a location (median) of <code>local</code> and scale factor of <code>scale</code>.</p>
<h3 id="jStat.chisquare">jStat.chisquare( dof )</h3>
<h4 id="jStat.chisquare.pdf">jStat.chisquare.pdf( x, dof )</h4>
<p>Returns the value of <code>x</code> in the pdf of the Chi Square distribution with <code>dof</code> degrees of freedom.</p>
<h4 id="jStat.chisquare.cdf">jStat.chisquare.cdf( x, dof )</h4>
<p>Returns the value of <code>x</code> in the cdf of the Chi Square distribution with <code>dof</code> degrees of freedom.</p>
<h4 id="jStat.chisquare.inv">jStat.chisquare.inv( p, dof )</h4>
<p>Returns the value of <code>x</code> in the inverse of the cdf for the Chi Square distribution with <code>dof</code> degrees of freedom.</p>
<h4 id="jStat.chisquare.mean">jStat.chisquare.mean( dof )</h4>
<p>Returns the value of the mean for the Chi Square distribution with <code>dof</code> degrees of freedom.</p>
<h4 id="jStat.chisquare.median">jStat.chisquare.median( dof )</h4>
<p>Returns the value of the median for the Chi Square distribution with <code>dof</code> degrees of freedom.</p>
<h4 id="jStat.chisquare.mode">jStat.chisquare.mode( dof )</h4>
<p>Returns the value of the mode for the Chi Square distribution with <code>dof</code> degrees of freedom.</p>
<h4 id="jStat.chisquare.sample">jStat.chisquare.sample( dof )</h4>
<p>Returns a random number whose distribution is the Chi Square distribution with <code>dof</code> degrees of freedom.</p>
<h4 id="jStat.chisquare.variance">jStat.chisquare.variance( dof )</h4>
<p>Returns the value of the variance for the Chi Square distribution with <code>dof</code> degrees of freedom.</p>
<h3 id="jStat.exponential">jStat.exponential( rate )</h3>
<h4 id="jStat.exponential.pdf">jStat.exponential.pdf( x, rate )</h4>
<p>Returns the value of <code>x</code> in the pdf of the Exponential distribution with the parameter <code>rate</code> (lambda).</p>
<h4 id="jStat.exponential.cdf">jStat.exponential.cdf( x, rate )</h4>
<p>Returns the value of <code>x</code> in the cdf of the Exponential distribution with the parameter <code>rate</code> (lambda).</p>
<h4 id="jStat.exponential.inv">jStat.exponential.inv( p, rate )</h4>
<p>Returns the value of <code>p</code> in the inverse of the cdf for the Exponential distribution with the parameter <code>rate</code> (lambda).</p>
<h4 id="jStat.exponential.mean">jStat.exponential.mean( rate )</h4>
<p>Returns the value of the mean for the Exponential distribution with the parameter <code>rate</code> (lambda).</p>
<h4 id="jStat.exponential.median">jStat.exponential.median( rate )</h4>
<p>Returns the value of the median for the Exponential distribution with the parameter <code>rate</code> (lambda)</p>
<h4 id="jStat.exponential.mode">jStat.exponential.mode( rate )</h4>
<p>Returns the value of the mode for the Exponential distribution with the parameter <code>rate</code> (lambda).</p>
<h4 id="jStat.exponential.sample">jStat.exponential.sample( rate )</h4>
<p>Returns a random number whose distribution is the Exponential distribution with the parameter <code>rate</code> (lambda).</p>
<h4 id="jStat.exponential.variance">jStat.exponential.variance( rate )</h4>
<p>Returns the value of the variance for the Exponential distribution with the parameter <code>rate</code> (lambda).</p>
<h3 id="jStat.gamma">jStat.gamma( shape, scale )</h3>
<h4 id="jStat.gamma.pdf">jStat.gamma.pdf( x, shape, scale )</h4>
<p>Returns the value of <code>x</code> in the pdf of the Gamma distribution with the parameters <code>shape</code> (k) and <code>scale</code> (theta). Notice that if using the alpha beta convention, <code>scale = 1/beta</code>.</p>
<h4 id="jStat.gamma.cdf">jStat.gamma.cdf( x, shape, scale )</h4>
<p>Returns the value of <code>x</code> in the cdf of the Gamma distribution with the parameters <code>shape</code> (k) and <code>scale</code> (theta). Notice that if using the alpha beta convention, <code>scale = 1/beta</code>.</p>
<p>This function is checked against R's <code>pgamma</code> function.</p>
<h4 id="jStat.gamma.inv">jStat.gamma.inv( p, shape, scale )</h4>
<p>Returns the value of <code>p</code> in the inverse of the cdf for the Gamma distribution with the parameters <code>shape</code> (k) and <code>scale</code> (theta). Notice that if using the alpha beta convention, <code>scale = 1/beta</code>.</p>
<p>This function is checked against R's <code>qgamma</code> function.</p>
<h4 id="jStat.gamma.mean">jStat.gamma.mean( shape, scale )</h4>
<p>Returns the value of the mean for the Gamma distribution with the parameters <code>shape</code> (k) and <code>scale</code> (theta). Notice that if using the alpha beta convention, <code>scale = 1/beta</code>.</p>
<h4 id="jStat.gamma.mode">jStat.gamma.mode( shape, scale )</h4>
<p>Returns the value of the mode for the Gamma distribution with the parameters <code>shape</code> (k) and <code>scale</code> (theta). Notice that if using the alpha beta convention, <code>scale = 1/beta</code>.</p>
<h4 id="jStat.gamma.sample">jStat.gamma.sample( shape, scale )</h4>
<p>Returns a random number whose distribution is the Gamma distribution with the parameters <code>shape</code> (k) and <code>scale</code> (theta). Notice that if using the alpha beta convention, <code>scale = 1/beta</code>.</p>
<h4 id="jStat.gamma.variance">jStat.gamma.variance( shape, scale )</h4>
<p>Returns the value of the variance for the Gamma distribution with the parameters <code>shape</code> (k) and <code>scale</code> (theta). Notice that if using the alpha beta convention, <code>scale = 1/beta</code>.</p>
<h3 id="jStat.invgamma">jStat.invgamma( shape, scale )</h3>
<h4 id="jStat.invgamma.pdf">jStat.invgamma.pdf( x, shape, scale )</h4>
<p>Returns the value of <code>x</code> in the pdf of the Inverse-Gamma distribution with parametres <code>shape</code> (alpha) and <code>scale</code> (beta).</p>
<h4 id="jStat.invgamma.cdf">jStat.invgamma.cdf( x, shape, scale )</h4>
<p>Returns the value of <code>x</code> in the cdf of the Inverse-Gamma distribution with parametres <code>shape</code> (alpha) and <code>scale</code> (beta).</p>
<h4 id="jStat.invgamma.inv">jStat.invgamma.inv( p, shape, scale )</h4>
<p>Returns the value of <code>p</code> in the inverse of the cdf for the Inverse-Gamma distribution with parametres <code>shape</code> (alpha) and <code>scale</code> (beta).</p>
<h4 id="jStat.invgamma.mean">jStat.invgamma.mean( shape, scale )</h4>
<p>Returns the value of the mean for the Inverse-Gamma distribution with parametres <code>shape</code> (alpha) and <code>scale</code> (beta).</p>
<h4 id="jStat.invgamma.mode">jStat.invgamma.mode( shape, scale )</h4>
<p>Returns the value of the mode for the Inverse-Gamma distribution with parametres <code>shape</code> (alpha) and <code>scale</code> (beta).</p>
<h4 id="jStat.invgamma.sample">jStat.invgamma.sample( shape, scale )</h4>
<p>Returns a random number whose distribution is the Inverse-Gamma distribution with parametres <code>shape</code> (alpha) and <code>scale</code> (beta).</p>
<h4 id="jStat.invgamma.variance">jStat.invgamma.variance( shape, scale )</h4>
<p>Returns the value of the variance for the Inverse-Gamma distribution with parametres <code>shape</code> (alpha) and <code>scale</code> (beta).</p>
<h3 id="jStat.kumaraswamy">jStat.kumaraswamy( alpha, beta )</h3>
<h4 id="jStat.kumaraswamy.pdf">jStat.kumaraswamy.pdf( x, a, b )</h4>
<p>Returns the value of <code>x</code> in the pdf of the Kumaraswamy distribution with parameters <code>a</code> and <code>b</code>.</p>
<h4 id="jStat.kumaraswamy.cdf">jStat.kumaraswamy.cdf( x, alpha, beta )</h4>
<p>Returns the value of <code>x</code> in the cdf of the Kumaraswamy distribution with parameters <code>alpha</code> and <code>beta</code>.</p>
<h4 id="jStat.kumaraswamy.inv">jStat.kumaraswamy.inv( p, alpha, beta )</h4>
<p>Returns the value of <code>p</code> in the inverse of the pdf for the Kumaraswamy distribution with parametres <code>alpha</code> and <code>beta</code>.</p>
<p>This function corresponds to <code>qkumar(p, alpha, beta)</code> in R's VGAM package.</p>
<h4 id="jStat.kumaraswamy.mean">jStat.kumaraswamy.mean( alpha, beta )</h4>
<p>Returns the value of the mean of the Kumaraswamy distribution with parameters <code>alpha</code> and <code>beta</code>.</p>
<h4 id="jStat.kumaraswamy.median">jStat.kumaraswamy.median( alpha, beta )</h4>
<p>Returns the value of the median of the Kumaraswamy distribution with parameters <code>alpha</code> and <code>beta</code>.</p>
<h4 id="jStat.kumaraswamy.mode">jStat.kumaraswamy.mode( alpha, beta )</h4>
<p>Returns the value of the mode of the Kumaraswamy distribution with parameters <code>alpha</code> and <code>beta</code>.</p>
<h4 id="jStat.kumaraswamy.variance">jStat.kumaraswamy.variance( alpha, beta )</h4>
<p>Returns the value of the variance of the Kumaraswamy distribution with parameters <code>alpha</code> and <code>beta</code>.</p>
<h3 id="jStat.lognormal">jStat.lognormal( mu, sigma )</h3>
<h4 id="jStat.lognormal.pdf">jStat.lognormal.pdf( x, mu, sigma )</h4>
<p>Returns the value of <code>x</code> in the pdf of the Log-normal distribution with paramters <code>mu</code> (mean) and <code>sigma</code> (standard deviation).</p>
<h4 id="jStat.lognormal.cdf">jStat.lognormal.cdf( x, mu, sigma )</h4>
<p>Returns the value of <code>x</code> in the cdf of the Log-normal distribution with paramters <code>mu</code> (mean) and <code>sigma</code> (standard deviation).</p>
<h4 id="jStat.lognormal.inv">jStat.lognormal.inv( p, mu, sigma )</h4>
<p>Returns the value of <code>x</code> in the inverse of the cdf for the Log-normal distribution with paramters <code>mu</code> (mean of the Normal distribution) and <code>sigma</code> (standard deviation of the Normal distribution).</p>
<h4 id="jStat.lognormal.mean">jStat.lognormal.mean( mu, sigma )</h4>
<p>Returns the value of the mean for the Log-normal distribution with paramters <code>mu</code> (mean of the Normal distribution) and <code>sigma</code> (standard deviation of the Normal distribution).</p>
<h4 id="jStat.lognormal.median">jStat.lognormal.median( mu, sigma )</h4>
<p>Returns the value of the median for the Log-normal distribution with paramters <code>mu</code> (mean of the Normal distribution) and <code>sigma</code> (standard deviation of the Normal distribution).</p>
<h4 id="jStat.lognormal.mode">jStat.lognormal.mode( mu, sigma )</h4>
<p>Returns the value of the mode for the Log-normal distribution with paramters <code>mu</code> (mean of the Normal distribution) and <code>sigma</code> (standard deviation of the Normal distribution).</p>
<h4 id="jStat.lognormal.sample">jStat.lognormal.sample( mu, sigma )</h4>
<p>Returns a random number whose distribution is the Log-normal distribution with paramters <code>mu</code> (mean of the Normal distribution) and <code>sigma</code> (standard deviation of the Normal distribution).</p>
<h4 id="jStat.lognormal.variance">jStat.lognormal.variance( mu, sigma )</h4>
<p>Returns the value of the variance for the Log-normal distribution with paramters <code>mu</code> (mean of the Normal distribution) and <code>sigma</code> (standard deviation of the Normal distribution).</p>
<h3 id="jStat.normal">jStat.normal( mean, std )</h3>
<h4 id="jStat.normal.pdf">jStat.normal.pdf( x, mean, std )</h4>
<p>Returns the value of <code>x</code> in the pdf of the Normal distribution with parameters <code>mean</code> and <code>std</code> (standard deviation).</p>
<h4 id="jStat.normal.cdf">jStat.normal.cdf( x, mean, std )</h4>
<p>Returns the value of <code>x</code> in the cdf of the Normal distribution with parameters <code>mean</code> and <code>std</code> (standard deviation).</p>
<h4 id="jStat.normal.inv">jStat.normal.inv( p, mean, std )</h4>
<p>Returns the value of <code>p</code> in the inverse cdf for the Normal distribution with parameters <code>mean</code> and <code>std</code> (standard deviation).</p>
<h4 id="jStat.normal.mean">jStat.normal.mean( mean, std )</h4>
<p>Returns the value of the mean for the Normal distribution with parameters <code>mean</code> and <code>std</code> (standard deviation).</p>
<h4 id="jStat.normal.median">jStat.normal.median( mean, std )</h4>
<p>Returns the value of the median for the Normal distribution with parameters <code>mean</code> and <code>std</code> (standard deviation).</p>
<h4 id="jStat.normal.mode">jStat.normal.mode( mean, std )</h4>
<p>Returns the value of the mode for the Normal distribution with parameters <code>mean</code> and <code>std</code> (standard deviation).</p>
<h4 id="jStat.normal.sample">jStat.normal.sample( mean, std )</h4>
<p>Returns a random number whose distribution is the Normal distribution with parameters <code>mean</code> and <code>std</code> (standard deviation).</p>
<h4 id="jStat.normal.variance">jStat.normal.variance( mean, std )</h4>
<p>Returns the value of the variance for the Normal distribution with parameters <code>mean</code> and <code>std</code> (standard deviation).</p>
<h3 id="jStat.pareto">jStat.pareto( scale, shape )</h3>
<h4 id="jStat.pareto.pdf">jStat.pareto.pdf( x, scale, shape )</h4>
<p>Returns the value of <code>x</code> in the pdf of the Pareto distribution with parameters <code>scale</code> (x<sub>m</sub>) and <code>shape</code> (alpha).</p>
<h4 id="jStat.pareto.inv">jStat.pareto.inv( p, scale, shape )</h4>
<p>Returns the inverse of the Pareto distribution with probability <code>p</code>, <code>scale</code>, <code>shape</code>.</p>
<p>This coresponds to <code>qpareto(p, scale, shape)</code> in R's VGAM package, and generally corresponds to the <code>q</code><dist> function pattern in R.</p>
<h4 id="jStat.pareto.cdf">jStat.pareto.cdf( x, scale, shape )</h4>
<p>Returns the value of <code>x</code> in the cdf of the Pareto distribution with parameters <code>scale</code> (x<sub>m</sub>) and <code>shape</code> (alpha).</p>
<h4 id="jStat.pareto.mean">jStat.pareto.mean( scale, shape )</h4>
<p>Returns the value of the mean of the Pareto distribution with parameters <code>scale</code> (x<sub>m</sub>) and <code>shape</code> (alpha).</p>
<h4 id="jStat.pareto.median">jStat.pareto.median( scale, shape )</h4>
<p>Returns the value of the median of the Pareto distribution with parameters <code>scale</code> (x<sub>m</sub>) and <code>shape</code> (alpha).</p>
<h4 id="jStat.pareto.mode">jStat.pareto.mode( scale, shape )</h4>
<p>Returns the value of the mode of the Pareto distribution with parameters <code>scale</code> (x<sub>m</sub>) and <code>shape</code> (alpha).</p>
<h4 id="jStat.pareto.variance">jStat.pareto.variance( scale, shape )</h4>
<p>Returns the value of the variance of the Pareto distribution with parameters <code>scale</code> (x<sub>m</sub>) and <code>shape</code> (alpha).</p>
<h3 id="jStat.studentt">jStat.studentt( dof )</h3>
<h4 id="jStat.studentt.pdf">jStat.studentt.pdf( x, dof )</h4>
<p>Returns the value of <code>x</code> in the pdf of the Student's T distribution with <code>dof</code> degrees of freedom.</p>
<h4 id="jStat.studentt.cdf">jStat.studentt.cdf( x, dof )</h4>
<p>Returns the value of <code>x</code> in the cdf of the Student's T distribution with <code>dof</code> degrees of freedom.</p>
<h4 id="jStat.studentt.inv">jStat.studentt.inv( p, dof )</h4>
<p>Returns the value of <code>p</code> in the inverse of the cdf for the Student's T distribution with <code>dof</code> degrees of freedom.</p>
<h4 id="jStat.studentt.mean">jStat.studentt.mean( dof )</h4>
<p>Returns the value of the mean of the Student's T distribution with <code>dof</code> degrees of freedom.</p>
<h4 id="jStat.studentt.median">jStat.studentt.median( dof )</h4>
<p>Returns the value of the median of the Student's T distribution with <code>dof</code> degrees of freedom.</p>
<h4 id="jStat.studentt.mode">jStat.studentt.mode( dof )</h4>
<p>Returns the value of the mode of the Student's T distribution with <code>dof</code> degrees of freedom.</p>
<h4 id="jStat.studentt.sample">jStat.studentt.sample( dof )</h4>
<p>Returns a random number whose distribution is the Student's T distribution with <code>dof</code> degrees of freedom.</p>
<h4 id="jStat.studentt.variance">jStat.studentt.variance( dof )</h4>
<p>Returns the value of the variance for the Student's T distribution with <code>dof</code> degrees of freedom.</p>
<h3 id="jStat.tukey">jStat.tukey( nmeans, dof )</h3>
<h4 id="jStat.tukey.cdf">jStat.tukey.cdf( q, nmeans, dof )</h4>
<p>Returns the value of q in the cdf of the Studentized range distribution with <code>nmeans</code> number of groups nmeans and <code>dof</code> degrees of freedom.</p>
<h4 id="jStat.tukey.inv">jStat.tukey.inv( p, nmeans, dof )</h4>
<p>Returns the value of <code>p</code> in the inverse of the cdf for the Studentized range distribution with <code>nmeans</code> number of groups and <code>dof</code> degrees of freedom.
Only accurate to 4 decimal places.</p>
<h3 id="jStat.weibull">jStat.weibull( scale, shape )</h3>
<h4 id="jStat.weibull.pdf">jStat.weibull.pdf( x, scale, shape )</h4>
<p>Returns the value <code>x</code> in the pdf for the Weibull distribution with parameters <code>scale</code> (lambda) and <code>shape</code> (k).</p>
<h4 id="jStat.weibull.cdf">jStat.weibull.cdf( x, scale, shape )</h4>
<p>Returns the value <code>x</code> in the cdf for the Weibull distribution with parameters <code>scale</code> (lambda) and <code>shape</code> (k).</p>
<h4 id="jStat.weibull.inv">jStat.weibull.inv( p, scale, shape )</h4>
<p>Returns the value of <code>x</code> in the inverse of the cdf for the Weibull distribution with parameters <code>scale</code> (lambda) and <code>shape</code> (k).</p>
<h4 id="jStat.weibull.mean">jStat.weibull.mean( scale, shape )</h4>
<p>Returns the value of the mean of the Weibull distribution with parameters <code>scale</code> (lambda) and <code>shape</code> (k).</p>
<h4 id="jStat.weibull.median">jStat.weibull.median( scale, shape )</h4>
<p>Returns the value of the median of the Weibull distribution with parameters <code>scale</code> (lambda) and <code>shape</code> (k).</p>
<h4 id="jStat.weibull.mode">jStat.weibull.mode( scale, shape )</h4>
<p>Returns the mode of the Weibull distribution with parameters <code>scale</code> (lambda) and <code>shape</code> (k).</p>
<h4 id="jStat.weibull.sample">jStat.weibull.sample( scale, shape )</h4>
<p>Returns a random number whose distribution is the Weibull distribution with parameters <code>scale</code> (lambda) and <code>shape</code> (k).</p>
<h4 id="jStat.weibull.variance">jStat.weibull.variance( scale, shape )</h4>
<p>Returns the variance of the Weibull distribution with parameters <code>scale</code> (lambda) and <code>shape</code> (k).</p>
<h3 id="jStat.uniform">jStat.uniform( a, b )</h3>
<h4 id="jStat.uniform.pdf">jStat.uniform.pdf( x, a, b )</h4>
<p>Returns the value of <code>x</code> in the pdf of the Uniform distribution from <code>a</code> to <code>b</code>.</p>
<h4 id="jStat.uniform.cdf">jStat.uniform.cdf( x, a, b )</h4>
<p>Returns the value of <code>x</code> in the cdf of the Uniform distribution from <code>a</code> to <code>b</code>.</p>
<h4 id="jStat.uniform.inv">jStat.uniform.inv( p, a, b)</h4>
<p>Returns the inverse of the <code>uniform.cdf</code> function; i.e. the value of <code>x</code> for which <code>uniform.cdf(x, a, b) == p</code>.</p>
<h4 id="jStat.uniform.mean">jStat.uniform.mean( a, b )</h4>
<p>Returns the value of the mean of the Uniform distribution from <code>a</code> to <code>b</code>.</p>
<h4 id="jStat.uniform.median">jStat.uniform.median( a, b )</h4>
<p>Returns the value of the median of the Uniform distribution from <code>a</code> to <code>b</code>.</p>
<h4 id="jStat.uniform.mode">jStat.uniform.mode( a, b )</h4>
<p>Returns the value of the mode of the Uniform distribution from <code>a</code> to <code>b</code>.</p>
<h4 id="jStat.uniform.sample">jStat.uniform.sample( a, b )</h4>
<p>Returns a random number whose distribution is the Uniform distribution from <code>a</code> to <code>b</code>.</p>
<h4 id="jStat.uniform.variance">jStat.uniform.variance( a, b )</h4>
<p>Returns the variance of the Uniform distribution from <code>a</code> to <code>b</code>.</p>
<h3 id="jStat.binomial">jStat.binomial</h3>
<h4 id="jStat.binomial.pdf">jStat.binomial.pdf( k, n, p )</h4>
<p>Returns the value of <code>k</code> in the pdf of the Binomial distribution with parameters <code>n</code> and <code>p</code>.</p>
<h4 id="jStat.binomial.cdf">jStat.binomial.cdf( k, n, p )</h4>
<p>Returns the value of <code>k</code> in the cdf of the Binomial distribution with parameters <code>n</code> and <code>p</code>.</p>
<h3 id="jStat.negbin">jStat.negbin</h3>
<h4 id="jStat.negbin.pdf">jStat.negbin.pdf( k, r, p )</h4>
<p>Returns the value of <code>k</code> in the pdf of the Negative Binomial distribution with parameters <code>n</code> and <code>p</code>.</p>
<h4 id="jStat.negbin.cdf">jStat.negbin.cdf( x, r, p )</h4>
<p>Returns the value of <code>x</code> in the cdf of the Negative Binomial distribution with parameters <code>n</code> and <code>p</code>.</p>
<h3 id="jStat.hypgeom">jStat.hypgeom</h3>
<h4 id="jStat.hypgeom.pdf">jStat.hypgeom.pdf( k, N, m, n )</h4>
<p>Returns the value of <code>k</code> in the pdf of the Hypergeometric distribution with parameters <code>N</code> (the population size), <code>m</code> (the success rate), and <code>n</code> (the number of draws).</p>
<h4 id="jStat.hypgeom.cdf">jStat.hypgeom.cdf( x, N, m, n )</h4>
<p>Returns the value of <code>x</code> in the cdf of the Hypergeometric distribution with parameters <code>N</code> (the population size), <code>m</code> (the success rate), and <code>n</code> (the number of draws).</p>
<h3 id="jStat.poisson">jStat.poisson</h3>
<h4 id="jStat.poisson.pdf">jStat.poisson.pdf( k, l )</h4>
<p>Returns the value of <code>k</code> in the pdf of the Poisson distribution with parameter <code>l</code> (lambda).</p>
<h4 id="jStat.poisson.cdf">jStat.poisson.cdf( x, l )</h4>
<p>Returns the value of <code>x</code> in the cdf of the Poisson distribution with parameter <code>l</code> (lambda).</p>
<h4 id="jStat.poisson.sample">jStat.poisson.sample( l )</h4>
<p>Returns a random number whose distribution is the Poisson distribution with rate parameter l (lamda)</p>
<h3 id="jStat.triangular">jStat.triangular</h3>
<h4 id="jStat.triangular.pdf">jStat.triangular.pdf( x, a, b, c )</h4>
<p>Returns the value of <code>x</code> in the pdf of the Triangular distribution with the parameters <code>a</code>, <code>b</code>, and <code>c</code>.</p>
<h4 id="jStat.triangular.cdf">jStat.triangular.cdf( x, a, b, c )</h4>
<p>Returns the value of <code>x</code> in the cdf of the Triangular distribution with the parameters <code>a</code>, <code>b</code>, and <code>c</code>.</p>
<h4 id="jStat.triangular.mean">jStat.triangular.mean( a, b, c )</h4>
<p>Returns the value of the mean of the Triangular distribution with the parameters <code>a</code>, <code>b</code>, and <code>c</code>.</p>
<h4 id="jStat.triangular.median">jStat.triangular.median( a, b, c )</h4>
<p>Returns the value of the median of the Triangular distribution with the parameters <code>a</code>, <code>b</code>, and <code>c</code>.</p>
<h4 id="jStat.triangular.mode">jStat.triangular.mode( a, b, c )</h4>
<p>Returns the value of the mode of the Triangular distribution with the parameters <code>a</code>, <code>b</code>, and <code>c</code>.</p>
<h4 id="jStat.triangular.sample">jStat.triangular.sample( a, b, c )</h4>
<p>Returns a random number whose distribution is the Triangular distribution with the parameters <code>a</code>, <code>b</code>, and <code>c</code>.</p>
<h4 id="jStat.triangular.variance">jStat.triangular.variance( a, b, c )</h4>
<p>Returns the value of the variance of the Triangular distribution with the parameters <code>a</code>, <code>b</code>, and <code>c</code>.</p>
<h3 id="jStat.arcsine">jStat.arcsine( a, b )</h3>
<h4 id="jStat.arcsine.pdf">jStat.arcsine.pdf( x, a, b )</h4>
<p>Returns the value of <code>x</code> in the pdf of the arcsine distribution from <code>a</code> to <code>b</code>.</p>
<h4 id="jStat.arcsine.cdf">jStat.arcsine.cdf( x, a, b )</h4>
<p>Returns the value of <code>x</code> in the cdf of the arcsine distribution from <code>a</code> to <code>b</code>.</p>
<h4 id="jStat.arcsine.inv">jStat.arcsine.inv(p, a, b)</h4>
<p>Returns the inverse of the <code>arcsine.cdf</code> function; i.e. the value of <code>x</code> for which <code>arcsine.cdf(x, a, b) == p</code>.</p>
<h4 id="jStat.arcsine.mean">jStat.arcsine.mean( a, b )</h4>
<p>Returns the value of the mean of the arcsine distribution from <code>a</code> to <code>b</code>.</p>
<h4 id="jStat.arcsine.median">jStat.arcsine.median( a, b )</h4>
<p>Returns the value of the median of the arcsine distribution from <code>a</code> to <code>b</code>.</p>
<h4 id="jStat.arcsine.mode">jStat.arcsine.mode( a, b )</h4>
<p>Returns the value of the mode of the arcsine distribution from <code>a</code> to <code>b</code>.</p>
<h4 id="jStat.arcsine.sample">jStat.arcsine.sample( a, b )</h4>
<p>Returns a random number whose distribution is the arcsine distribution from <code>a</code> to <code>b</code>.</p>
<h4 id="jStat.arcsine.variance">jStat.arcsine.variance( a, b )</h4>
<p>Returns the variance of the Uniform distribution from <code>a</code> to <code>b</code>.</p>
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