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<!DOCTYPE html> <html lang="en"> <head> <title>Probability -- basic probability functions</title> <meta content="text/html; charset=utf-8" http-equiv="Content-Type"> <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css"> <link rel="stylesheet" href="../../../../Macaulay2/Style/katex/katex.min.css"> <script defer="defer" src="../../../../Macaulay2/Style/katex/katex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> <script> var macros = { "\\break": "\\\\", "\\ZZ": "\\mathbb{Z}", "\\NN": "\\mathbb{N}", "\\QQ": "\\mathbb{Q}", "\\RR": "\\mathbb{R}", "\\CC": "\\mathbb{C}", "\\PP": "\\mathbb{P}" }, delimiters = [ { left: "$$", right: "$$", display: true}, { left: "\\[", right: "\\]", display: true}, { left: "$", right: "$", display: false}, { left: "\\(", right: "\\)", display: false} ], ignoredTags = [ "kbd", "var", "samp", "script", "noscript", "style", "textarea", "pre", "code", "option" ]; document.addEventListener("DOMContentLoaded", function() { renderMathInElement(document.body, { delimiters: delimiters, macros: macros, ignoredTags: ignoredTags, trust: true }); }); </script> <style>.katex { font-size: 1em; }</style> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/copy-tex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/render-a11y-string.min.js"></script> <script src="../../../../Macaulay2/Style/prism.js"></script> <script>var current_version = '1.25.06';</script> <script src="../../../../Macaulay2/Style/version-select.js"></script> <link type="image/x-icon" rel="icon" href="../../../../Macaulay2/Style/icon.gif"> </head> <body> <div id="buttons"> <div> <a href="https://macaulay2.com/">Macaulay2</a> <span id="version-select-container"></span> » <a title="Macaulay2 documentation" href="../../Macaulay2Doc/html/index.html">Documentation </a> <br><a href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a title="basic probability functions" href="index.html">Probability</a> :: <a title="basic probability functions" href="index.html">Probability</a></span> </div> <div class="right"> <form method="get" action="https://www.google.com/search"> <input placeholder="Search" type="text" name="q" value=""> <input type="hidden" name="q" value="site:macaulay2.com/doc"> </form> next | previous | <a href="___Probability__Distribution.html">forward</a> | backward | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <div> <h1>Probability -- basic probability functions</h1> <div> <h2>Description</h2> <div> <p>This package provides a number of basic probability functions. In particular, for both discrete and continuous probability distributions, there are the following four functions:</p> <ul> <li><a title="probability density (or mass) function" href="_density.html">density</a>: probability density (or mass) function</li> <li><a title="cumulative distribution function" href="_probability.html">probability</a>: cumulative distribution function</li> <li><a title="quantile function" href="_quantile.html">quantile</a>: quantile function</li> <li><a title="randomly generate samples from probability distribution" href="_random_lp__Probability__Distribution_rp.html">random(ProbabilityDistribution)</a>: generate random samples</li> </ul> <p>A variety of common probability distributions are supported.</p> <h3>Discrete distributions</h3> <ul> <li><a title="binomial distribution" href="_binomial__Distribution.html">binomial</a></li> <li><a title="Poisson distribution" href="_poisson__Distribution.html">Poisson</a></li> <li><a title="geometric distribution" href="_geometric__Distribution.html">geometric</a></li> <li><a title="negative binomial distribution" href="_negative__Binomial__Distribution.html">negative binomial</a></li> <li><a title="hypergeometric distribution" href="_hypergeometric__Distribution.html">hypergeometric</a></li> </ul> <h3>Continuous distributions</h3> <ul> <li><a title="continuous uniform distribution" href="_uniform__Distribution.html">uniform</a></li> <li><a title="exponential distribution" href="_exponential__Distribution.html">exponential</a></li> <li><a title="normal distribution" href="_normal__Distribution.html">normal</a></li> <li><a title="gamma distribution" href="_gamma__Distribution.html">gamma</a></li> <li><a title="chi-squared distribution" href="_chi__Squared__Distribution.html">chi-squared</a></li> <li><a title="Student's t-distribution" href="_t__Distribution.html">Student's t</a></li> <li><a title="F-distribution" href="_f__Distribution.html">F</a></li> <li><a title="beta distribution" href="_beta__Distribution.html">beta</a></li> </ul> <p>You may also define your own probability distributions using <a title="construct a discrete probability distribution" href="_discrete__Probability__Distribution.html">discreteProbabilityDistribution</a> and <a title="construct a continuous probability distribution" href="_continuous__Probability__Distribution.html">continuousProbabilityDistribution</a>.</p> </div> </div> <div> <h2>Caveat</h2> <div> <p>As is always the case when working with real numbers in Macaulay2, unexpected results may occur due to the limitations of floating point arithmetic.</p> </div> </div> <div> <h3>Menu</h3> <ul> <li><span><a title="probability distribution class" href="___Probability__Distribution.html">ProbabilityDistribution</a> -- probability distribution class</span></li> </ul> </div> <div> <div> <div> <h2>Author</h2> <ul> <li><a href="https://webwork.piedmont.edu/~dtorrance">Doug Torrance</a><span> <<a href="mailto:dtorrance%40piedmont.edu">dtorrance@piedmont.edu</a>></span></li> </ul> </div> <div> <h2>Certification <img src="../../../../Macaulay2/Style/GoldStar.png" alt="a gold star"> </h2> <p>Version <b>0.3</b> of this package was accepted for publication in <a href="https://msp.org/jsag/2024/14-1/">volume 14</a> of <a href="https://msp.org/jsag/">Journal of Software for Algebra and Geometry</a> on 2024-01-23, in the article <a href="https://msp.org/jsag/2024/14-1/p07.xhtml">The Probability package for Macaulay2</a> (DOI: <a href="https://doi.org/10.2140/jsag.2024.14.51">10.2140/jsag.2024.14.51</a>). That version can be obtained from <a href="https://msp.org/jsag/2024/14-1/jsag-v14-n1-x07-Probability.m2">the journal</a>.</p> </div> <div> <h2>Version</h2> <p>This documentation describes version <b>0.5</b> of Probability, released <b>September 13, 2024</b>.</p> </div> <div> <h2>Citation</h2> <p>If you have used this package in your research, please cite it as follows:</p> <table class="examples"> <tr> <td> <pre><code class="language-bib">@misc{ProbabilitySource, title = {{Probability: basic probability functions. Version~0.5}}, author = {Doug Torrance}, howpublished = {A \emph{Macaulay2} package available at \url{https://github.com/Macaulay2/M2/tree/stable/M2/Macaulay2/packages}} } @article{ProbabilityArticle, title = {{The Probability package for \emph{Macaulay2}}}, author = {Doug Torrance}, journal = {Journal of Software for Algebra and Geometry}, volume = {14}, year = {2024}, } </code></pre> </td> </tr> </table> </div> <div> <h2>Exports</h2> <div class="exports"> <ul> <li>Types <ul> <li><span><kbd>ContinuousProbabilityDistribution</kbd> -- see <span><a title="probability distribution class" href="___Probability__Distribution.html">ProbabilityDistribution</a> -- probability distribution class</span></span></li> <li><span><kbd>DiscreteProbabilityDistribution</kbd> -- see <span><a title="probability distribution class" href="___Probability__Distribution.html">ProbabilityDistribution</a> -- probability distribution class</span></span></li> <li><span><a title="probability distribution class" href="___Probability__Distribution.html">ProbabilityDistribution</a> -- probability distribution class</span></li> </ul> </li> <li>Functions and commands <ul> <li><span><a title="beta distribution" href="_beta__Distribution.html">betaDistribution</a> -- beta distribution</span></li> <li><span><kbd>bernoulliDistribution</kbd> -- see <span><a title="binomial distribution" href="_binomial__Distribution.html">binomialDistribution</a> -- binomial distribution</span></span></li> <li><span><a title="binomial distribution" href="_binomial__Distribution.html">binomialDistribution</a> -- binomial distribution</span></li> <li><span><a title="chi-squared distribution" href="_chi__Squared__Distribution.html">chiSquaredDistribution</a> -- chi-squared distribution</span></li> <li><span><a title="construct a continuous probability distribution" href="_continuous__Probability__Distribution.html">continuousProbabilityDistribution</a> -- construct a continuous probability distribution</span></li> <li><span><a title="probability density (or mass) function" href="_density.html">density</a> -- probability density (or mass) function</span></li> <li><span><a title="construct a discrete probability distribution" href="_discrete__Probability__Distribution.html">discreteProbabilityDistribution</a> -- construct a discrete probability distribution</span></li> <li><span><a title="exponential distribution" href="_exponential__Distribution.html">exponentialDistribution</a> -- exponential distribution</span></li> <li><span><a title="F-distribution" href="_f__Distribution.html">fDistribution</a> -- F-distribution</span></li> <li><span><a title="gamma distribution" href="_gamma__Distribution.html">gammaDistribution</a> -- gamma distribution</span></li> <li><span><a title="geometric distribution" href="_geometric__Distribution.html">geometricDistribution</a> -- geometric distribution</span></li> <li><span><a title="hypergeometric distribution" href="_hypergeometric__Distribution.html">hypergeometricDistribution</a> -- hypergeometric distribution</span></li> <li><span><a title="negative binomial distribution" href="_negative__Binomial__Distribution.html">negativeBinomialDistribution</a> -- negative binomial distribution</span></li> <li><span><a title="normal distribution" href="_normal__Distribution.html">normalDistribution</a> -- normal distribution</span></li> <li><span><a title="Poisson distribution" href="_poisson__Distribution.html">poissonDistribution</a> -- Poisson distribution</span></li> <li><span><a title="cumulative distribution function" href="_probability.html">probability</a> -- cumulative distribution function</span></li> <li><span><a title="quantile function" href="_quantile.html">quantile</a> -- quantile function</span></li> <li><span><a title="Student's t-distribution" href="_t__Distribution.html">tDistribution</a> -- Student's t-distribution</span></li> <li><span><a title="continuous uniform distribution" href="_uniform__Distribution.html">uniformDistribution</a> -- continuous uniform distribution</span></li> </ul> </li> <li>Methods <ul> <li><span><kbd>betaDistribution(Number,Number)</kbd> -- see <span><a title="beta distribution" href="_beta__Distribution.html">betaDistribution</a> -- beta distribution</span></span></li> <li><span><kbd>bernoulliDistribution(Number)</kbd> -- see <span><a title="binomial distribution" href="_binomial__Distribution.html">binomialDistribution</a> -- binomial distribution</span></span></li> <li><span><kbd>binomialDistribution(ZZ,Number)</kbd> -- see <span><a title="binomial distribution" href="_binomial__Distribution.html">binomialDistribution</a> -- binomial distribution</span></span></li> <li><span><kbd>chiSquaredDistribution(Number)</kbd> -- see <span><a title="chi-squared distribution" href="_chi__Squared__Distribution.html">chiSquaredDistribution</a> -- chi-squared distribution</span></span></li> <li><span><kbd>continuousProbabilityDistribution(Function)</kbd> -- see <span><a title="construct a continuous probability distribution" href="_continuous__Probability__Distribution.html">continuousProbabilityDistribution</a> -- construct a continuous probability distribution</span></span></li> <li><span><kbd>density(DiscreteProbabilityDistribution,Number)</kbd> -- see <span><a title="probability density (or mass) function" href="_density.html">density</a> -- probability density (or mass) function</span></span></li> <li><span><kbd>density(ProbabilityDistribution,Number)</kbd> -- see <span><a title="probability density (or mass) function" href="_density.html">density</a> -- probability density (or mass) function</span></span></li> <li><span><kbd>discreteProbabilityDistribution(Function)</kbd> -- see <span><a title="construct a discrete probability distribution" href="_discrete__Probability__Distribution.html">discreteProbabilityDistribution</a> -- construct a discrete probability distribution</span></span></li> <li><span><kbd>exponentialDistribution(Number)</kbd> -- see <span><a title="exponential distribution" href="_exponential__Distribution.html">exponentialDistribution</a> -- exponential distribution</span></span></li> <li><span><kbd>fDistribution(Number,Number)</kbd> -- see <span><a title="F-distribution" href="_f__Distribution.html">fDistribution</a> -- F-distribution</span></span></li> <li><span><kbd>gammaDistribution(Number,Number)</kbd> -- see <span><a title="gamma distribution" href="_gamma__Distribution.html">gammaDistribution</a> -- gamma distribution</span></span></li> <li><span><kbd>geometricDistribution(Number)</kbd> -- see <span><a title="geometric distribution" href="_geometric__Distribution.html">geometricDistribution</a> -- geometric distribution</span></span></li> <li><span><kbd>hypergeometricDistribution(ZZ,ZZ,ZZ)</kbd> -- see <span><a title="hypergeometric distribution" href="_hypergeometric__Distribution.html">hypergeometricDistribution</a> -- hypergeometric distribution</span></span></li> <li><span><kbd>negativeBinomialDistribution(Number,Number)</kbd> -- see <span><a title="negative binomial distribution" href="_negative__Binomial__Distribution.html">negativeBinomialDistribution</a> -- negative binomial distribution</span></span></li> <li><span><kbd>normalDistribution(Number,Number)</kbd> -- see <span><a title="normal distribution" href="_normal__Distribution.html">normalDistribution</a> -- normal distribution</span></span></li> <li><span><kbd>poissonDistribution(Number)</kbd> -- see <span><a title="Poisson distribution" href="_poisson__Distribution.html">poissonDistribution</a> -- Poisson distribution</span></span></li> <li><span><kbd>probability(DiscreteProbabilityDistribution,Number)</kbd> -- see <span><a title="cumulative distribution function" href="_probability.html">probability</a> -- cumulative distribution function</span></span></li> <li><span><kbd>probability(ProbabilityDistribution,Number)</kbd> -- see <span><a title="cumulative distribution function" href="_probability.html">probability</a> -- cumulative distribution function</span></span></li> <li><span><kbd>net(ProbabilityDistribution)</kbd> -- see <span><a title="probability distribution class" href="___Probability__Distribution.html">ProbabilityDistribution</a> -- probability distribution class</span></span></li> <li><span><kbd>quantile(DiscreteProbabilityDistribution,Number)</kbd> -- see <span><a title="quantile function" href="_quantile.html">quantile</a> -- quantile function</span></span></li> <li><span><kbd>quantile(ProbabilityDistribution,Number)</kbd> -- see <span><a title="quantile function" href="_quantile.html">quantile</a> -- quantile function</span></span></li> <li><span><a title="randomly generate samples from probability distribution" href="_random_lp__Probability__Distribution_rp.html">random(ProbabilityDistribution)</a> -- randomly generate samples from probability distribution</span></li> <li><span><kbd>tDistribution(Number)</kbd> -- see <span><a title="Student's t-distribution" href="_t__Distribution.html">tDistribution</a> -- Student's t-distribution</span></span></li> <li><span><kbd>uniformDistribution(Number,Number)</kbd> -- see <span><a title="continuous uniform distribution" href="_uniform__Distribution.html">uniformDistribution</a> -- continuous uniform distribution</span></span></li> </ul> </li> <li>Symbols <ul> <li><span><a title="probability density function" href="___Density__Function.html">DensityFunction</a> -- probability density function</span></li> <li><span><a title="cumulative distribution function" href="___Distribution__Function.html">DistributionFunction</a> -- cumulative distribution function</span></li> <li><span><a title="whether to computer lower tail probabilities" href="___Lower__Tail.html">LowerTail</a> -- whether to computer lower tail probabilities</span></li> <li><span><a title="quantile function" href="___Quantile__Function.html">QuantileFunction</a> -- quantile function</span></li> <li><span><a title="random generation function" href="___Random__Generation.html">RandomGeneration</a> -- random generation function</span></li> <li><span><a title="support for probability distribution" href="___Support.html">Support</a> -- support for probability distribution</span></li> </ul> </li> </ul> </div> </div> </div> <div class="waystouse"> <h2>For the programmer</h2> <p>The object <a title="basic probability functions" href="index.html">Probability</a> is <span>a <a title="the class of all packages" href="../../Macaulay2Doc/html/___Package.html">package</a></span>, defined in <span class="tt">Probability.m2</span>.</p> </div> <hr> <div class="waystouse"> <p>The source of this document is in <span class="tt">Probability.m2:473:0</span>.</p> </div> </div> </div> </body> </html>
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