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<a href="../MathNet.Numerics.Distributions/Zipf.htm" class="current">Zipf</a>
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</ul>
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</div>
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</div>
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<div class="header">
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<p class="class"><strong>Type</strong> Zipf</p>
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<p><strong>Namespace</strong> MathNet.Numerics.Distributions</p>
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<p><strong>Interfaces</strong> <a href="../MathNet.Numerics.Distributions/IDiscreteDistribution.htm">IDiscreteDistribution</a></p>
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</div>
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<div class="sub-header">
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<div id="summary">Discrete Univariate Zipf distribution.
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Zipf's law, an empirical law formulated using mathematical statistics, refers to the fact
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that many types of data studied in the physical and social sciences can be approximated with
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a Zipfian distribution, one of a family of related discrete power law probability distributions.
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For details about this distribution, see.
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</div>
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<h3 class="section">Constructors</h3>
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<ul>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#.ctor">Zipf</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#.ctor">Zipf</a></li>
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</ul>
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<h3 class="section">Static Functions</h3>
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<ul>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#CDF">CDF</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#IsValidParameterSet">IsValidParameterSet</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#PMF">PMF</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#PMFLn">PMFLn</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#Sample">Sample</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#Sample">Sample</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#Samples">Samples</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#Samples">Samples</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#Samples">Samples</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#Samples">Samples</a></li>
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</ul>
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<h3 class="section">Methods</h3>
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<ul>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#CumulativeDistribution">CumulativeDistribution</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#Equals">Equals</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#GetHashCode">GetHashCode</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#GetType">GetType</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#Probability">Probability</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#ProbabilityLn">ProbabilityLn</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#Sample">Sample</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#Samples">Samples</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#Samples">Samples</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#ToString">ToString</a></li>
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</ul>
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<h3 class="section">Properties</h3>
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<ul>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#Entropy">Entropy</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#Maximum">Maximum</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#Mean">Mean</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#Median">Median</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#Minimum">Minimum</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#Mode">Mode</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#N">N</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#RandomSource">RandomSource</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#S">S</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#Skewness">Skewness</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#StdDev">StdDev</a></li>
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<li><a href="../MathNet.Numerics.Distributions/Zipf.htm#Variance">Variance</a></li>
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</ul>
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</div>
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<h3 class="section">Public Constructors</h3>
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<div id=".ctor" class="method">
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<h4> <strong>Zipf</strong>(<span title="System.double">double</span> s, <span title="System.int">int</span> n, <span title="System.Random">Random</span> randomSource)</h4>
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<div class="content">Initializes a new instance of the <a href="../MathNet.Numerics.Distributions/Zipf.htm">Zipf</a> class.
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><span title="System.double">double</span></code> s</h6>
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<p class="comments">The s parameter of the distribution. </p>
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<h6><code><span title="System.int">int</span></code> n</h6>
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<p class="comments">The n parameter of the distribution. </p>
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<h6><code><span title="System.Random">Random</span></code> randomSource</h6>
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<p class="comments">The random number generator which is used to draw random samples. </p>
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</div>
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</div>
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</div>
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<div id=".ctor" class="method">
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<h4> <strong>Zipf</strong>(<span title="System.double">double</span> s, <span title="System.int">int</span> n)</h4>
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<div class="content">Initializes a new instance of the <a href="../MathNet.Numerics.Distributions/Zipf.htm">Zipf</a> class.
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><span title="System.double">double</span></code> s</h6>
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<p class="comments">The s parameter of the distribution. </p>
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<h6><code><span title="System.int">int</span></code> n</h6>
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<p class="comments">The n parameter of the distribution. </p>
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</div>
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</div>
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</div>
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<h3 class="section">Public Static Functions</h3>
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<div id="CDF" class="method">
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<h4><span title="System.double">double</span> <strong>CDF</strong>(<span title="System.double">double</span> s, <span title="System.int">int</span> n, <span title="System.double">double</span> x)</h4>
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<div class="content">Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
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<div class="parameters">
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<h5>Parameters</h5>
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<h6><code><span title="System.double">double</span></code> s</h6>
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<p class="comments">The s parameter of the distribution. </p>
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<h6><code><span title="System.int">int</span></code> n</h6>
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<p class="comments">The n parameter of the distribution. </p>
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<h6><code><span title="System.double">double</span></code> x</h6>
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<p class="comments">The location at which to compute the cumulative distribution function. </p>
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|
</div>
|
|
|
|
<div class="return">
|
|
<h5>Return</h5>
|
|
<h6><code><span title="System.double">double</span></code></h6>
|
|
<p>the cumulative distribution at location <var>x</var>. </p>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
<div id="IsValidParameterSet" class="method">
|
|
<h4><span title="System.bool">bool</span> <strong>IsValidParameterSet</strong>(<span title="System.double">double</span> s, <span title="System.int">int</span> n)</h4>
|
|
<div class="content">Tests whether the provided values are valid parameters for this distribution.
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.double">double</span></code> s</h6>
|
|
<p class="comments">The s parameter of the distribution. </p>
|
|
<h6><code><span title="System.int">int</span></code> n</h6>
|
|
<p class="comments">The n parameter of the distribution. </p>
|
|
</div>
|
|
|
|
|
|
</div>
|
|
</div>
|
|
<div id="PMF" class="method">
|
|
<h4><span title="System.double">double</span> <strong>PMF</strong>(<span title="System.double">double</span> s, <span title="System.int">int</span> n, <span title="System.int">int</span> k)</h4>
|
|
<div class="content">Computes the probability mass (PMF) at k, i.e. P(X = k).
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.double">double</span></code> s</h6>
|
|
<p class="comments">The s parameter of the distribution. </p>
|
|
<h6><code><span title="System.int">int</span></code> n</h6>
|
|
<p class="comments">The n parameter of the distribution. </p>
|
|
<h6><code><span title="System.int">int</span></code> k</h6>
|
|
<p class="comments">The location in the domain where we want to evaluate the probability mass function. </p>
|
|
</div>
|
|
|
|
<div class="return">
|
|
<h5>Return</h5>
|
|
<h6><code><span title="System.double">double</span></code></h6>
|
|
<p>the probability mass at location <var>k</var>. </p>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
<div id="PMFLn" class="method">
|
|
<h4><span title="System.double">double</span> <strong>PMFLn</strong>(<span title="System.double">double</span> s, <span title="System.int">int</span> n, <span title="System.int">int</span> k)</h4>
|
|
<div class="content">Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.double">double</span></code> s</h6>
|
|
<p class="comments">The s parameter of the distribution. </p>
|
|
<h6><code><span title="System.int">int</span></code> n</h6>
|
|
<p class="comments">The n parameter of the distribution. </p>
|
|
<h6><code><span title="System.int">int</span></code> k</h6>
|
|
<p class="comments">The location in the domain where we want to evaluate the log probability mass function. </p>
|
|
</div>
|
|
|
|
<div class="return">
|
|
<h5>Return</h5>
|
|
<h6><code><span title="System.double">double</span></code></h6>
|
|
<p>the log probability mass at location <var>k</var>. </p>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Sample" class="method">
|
|
<h4><span title="System.int">int</span> <strong>Sample</strong>(<span title="System.Random">Random</span> rnd, <span title="System.double">double</span> s, <span title="System.int">int</span> n)</h4>
|
|
<div class="content">Samples a random variable.
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.Random">Random</span></code> rnd</h6>
|
|
<p class="comments">The random number generator to use. </p>
|
|
<h6><code><span title="System.double">double</span></code> s</h6>
|
|
<p class="comments">The s parameter of the distribution. </p>
|
|
<h6><code><span title="System.int">int</span></code> n</h6>
|
|
<p class="comments">The n parameter of the distribution. </p>
|
|
</div>
|
|
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Sample" class="method">
|
|
<h4><span title="System.int">int</span> <strong>Sample</strong>(<span title="System.double">double</span> s, <span title="System.int">int</span> n)</h4>
|
|
<div class="content">Samples a random variable.
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.double">double</span></code> s</h6>
|
|
<p class="comments">The s parameter of the distribution. </p>
|
|
<h6><code><span title="System.int">int</span></code> n</h6>
|
|
<p class="comments">The n parameter of the distribution. </p>
|
|
</div>
|
|
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Samples" class="method">
|
|
<h4><span title="System.void">void</span> <strong>Samples</strong>(<span title="System.Int32[]">Int32[]</span> values, <span title="System.double">double</span> s, <span title="System.int">int</span> n)</h4>
|
|
<div class="content">Fills an array with samples generated from the distribution.
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.Int32[]">Int32[]</span></code> values</h6>
|
|
<p class="comments">The array to fill with the samples. </p>
|
|
<h6><code><span title="System.double">double</span></code> s</h6>
|
|
<p class="comments">The s parameter of the distribution. </p>
|
|
<h6><code><span title="System.int">int</span></code> n</h6>
|
|
<p class="comments">The n parameter of the distribution. </p>
|
|
</div>
|
|
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Samples" class="method">
|
|
<h4><span title="System.void">void</span> <strong>Samples</strong>(<span title="System.Random">Random</span> rnd, <span title="System.Int32[]">Int32[]</span> values, <span title="System.double">double</span> s, <span title="System.int">int</span> n)</h4>
|
|
<div class="content">Fills an array with samples generated from the distribution.
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.Random">Random</span></code> rnd</h6>
|
|
<p class="comments">The random number generator to use. </p>
|
|
<h6><code><span title="System.Int32[]">Int32[]</span></code> values</h6>
|
|
<p class="comments">The array to fill with the samples. </p>
|
|
<h6><code><span title="System.double">double</span></code> s</h6>
|
|
<p class="comments">The s parameter of the distribution. </p>
|
|
<h6><code><span title="System.int">int</span></code> n</h6>
|
|
<p class="comments">The n parameter of the distribution. </p>
|
|
</div>
|
|
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Samples" class="method">
|
|
<h4><span title="System.Collections.Generic.IEnumerable<int>">IEnumerable<int></span> <strong>Samples</strong>(<span title="System.Random">Random</span> rnd, <span title="System.double">double</span> s, <span title="System.int">int</span> n)</h4>
|
|
<div class="content">Samples a sequence of this random variable.
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.Random">Random</span></code> rnd</h6>
|
|
<p class="comments">The random number generator to use. </p>
|
|
<h6><code><span title="System.double">double</span></code> s</h6>
|
|
<p class="comments">The s parameter of the distribution. </p>
|
|
<h6><code><span title="System.int">int</span></code> n</h6>
|
|
<p class="comments">The n parameter of the distribution. </p>
|
|
</div>
|
|
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Samples" class="method">
|
|
<h4><span title="System.Collections.Generic.IEnumerable<int>">IEnumerable<int></span> <strong>Samples</strong>(<span title="System.double">double</span> s, <span title="System.int">int</span> n)</h4>
|
|
<div class="content">Samples a sequence of this random variable.
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.double">double</span></code> s</h6>
|
|
<p class="comments">The s parameter of the distribution. </p>
|
|
<h6><code><span title="System.int">int</span></code> n</h6>
|
|
<p class="comments">The n parameter of the distribution. </p>
|
|
</div>
|
|
|
|
|
|
</div>
|
|
</div>
|
|
|
|
<h3 class="section">Public Methods</h3>
|
|
|
|
<div id="CumulativeDistribution" class="method">
|
|
<h4><span title="System.double">double</span> <strong>CumulativeDistribution</strong>(<span title="System.double">double</span> x)</h4>
|
|
<div class="content">Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.double">double</span></code> x</h6>
|
|
<p class="comments">The location at which to compute the cumulative distribution function. </p>
|
|
</div>
|
|
|
|
<div class="return">
|
|
<h5>Return</h5>
|
|
<h6><code><span title="System.double">double</span></code></h6>
|
|
<p>the cumulative distribution at location <var>x</var>. </p>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Equals" class="method">
|
|
<h4><span title="System.bool">bool</span> <strong>Equals</strong>(<span title="System.object">object</span> obj)</h4>
|
|
<div class="content">
|
|
|
|
|
|
|
|
|
|
</div>
|
|
</div>
|
|
<div id="GetHashCode" class="method">
|
|
<h4><span title="System.int">int</span> <strong>GetHashCode</strong>()</h4>
|
|
<div class="content">
|
|
|
|
|
|
|
|
|
|
</div>
|
|
</div>
|
|
<div id="GetType" class="method">
|
|
<h4><span title="System.Type">Type</span> <strong>GetType</strong>()</h4>
|
|
<div class="content">
|
|
|
|
|
|
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Probability" class="method">
|
|
<h4><span title="System.double">double</span> <strong>Probability</strong>(<span title="System.int">int</span> k)</h4>
|
|
<div class="content">Computes the probability mass (PMF) at k, i.e. P(X = k).
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.int">int</span></code> k</h6>
|
|
<p class="comments">The location in the domain where we want to evaluate the probability mass function. </p>
|
|
</div>
|
|
|
|
<div class="return">
|
|
<h5>Return</h5>
|
|
<h6><code><span title="System.double">double</span></code></h6>
|
|
<p>the probability mass at location <var>k</var>. </p>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
<div id="ProbabilityLn" class="method">
|
|
<h4><span title="System.double">double</span> <strong>ProbabilityLn</strong>(<span title="System.int">int</span> k)</h4>
|
|
<div class="content">Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
|
|
|
|
|
|
<div class="parameters">
|
|
<h5>Parameters</h5>
|
|
|
|
<h6><code><span title="System.int">int</span></code> k</h6>
|
|
<p class="comments">The location in the domain where we want to evaluate the log probability mass function. </p>
|
|
</div>
|
|
|
|
<div class="return">
|
|
<h5>Return</h5>
|
|
<h6><code><span title="System.double">double</span></code></h6>
|
|
<p>the log probability mass at location <var>k</var>. </p>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Sample" class="method">
|
|
<h4><span title="System.int">int</span> <strong>Sample</strong>()</h4>
|
|
<div class="content">Draws a random sample from the distribution.
|
|
|
|
|
|
|
|
<div class="return">
|
|
<h5>Return</h5>
|
|
<h6><code><span title="System.int">int</span></code></h6>
|
|
<p>a sample from the distribution. </p>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Samples" class="method">
|
|
<h4><span title="System.Collections.Generic.IEnumerable<int>">IEnumerable<int></span> <strong>Samples</strong>()</h4>
|
|
<div class="content">Samples an array of zipf distributed random variables.
|
|
|
|
|
|
|
|
<div class="return">
|
|
<h5>Return</h5>
|
|
<h6><code><span title="System.Collections.Generic.IEnumerable<int>">IEnumerable<int></span></code></h6>
|
|
<p>a sequence of samples from the distribution. </p>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Samples" class="method">
|
|
<h4><span title="System.void">void</span> <strong>Samples</strong>(<span title="System.Int32[]">Int32[]</span> values)</h4>
|
|
<div class="content">Fills an array with samples generated from the distribution.
|
|
|
|
|
|
|
|
|
|
</div>
|
|
</div>
|
|
<div id="ToString" class="method">
|
|
<h4><span title="System.string">string</span> <strong>ToString</strong>()</h4>
|
|
<div class="content">A string representation of the distribution.
|
|
|
|
|
|
|
|
<div class="return">
|
|
<h5>Return</h5>
|
|
<h6><code><span title="System.string">string</span></code></h6>
|
|
<p>a string representation of the distribution. </p>
|
|
</div>
|
|
|
|
</div>
|
|
</div>
|
|
|
|
<h3 class="section">Public Properties</h3>
|
|
|
|
<div id="Entropy" class="method">
|
|
<h4><span title="System.double">double</span> <strong>Entropy</strong> get; </h4>
|
|
<div class="content">Gets the entropy of the distribution.
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Maximum" class="method">
|
|
<h4><span title="System.int">int</span> <strong>Maximum</strong> get; </h4>
|
|
<div class="content">Gets the largest element in the domain of the distributions which can be represented by an integer.
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Mean" class="method">
|
|
<h4><span title="System.double">double</span> <strong>Mean</strong> get; </h4>
|
|
<div class="content">Gets the mean of the distribution.
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Median" class="method">
|
|
<h4><span title="System.double">double</span> <strong>Median</strong> get; </h4>
|
|
<div class="content">Gets the median of the distribution.
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Minimum" class="method">
|
|
<h4><span title="System.int">int</span> <strong>Minimum</strong> get; </h4>
|
|
<div class="content">Gets the smallest element in the domain of the distributions which can be represented by an integer.
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Mode" class="method">
|
|
<h4><span title="System.int">int</span> <strong>Mode</strong> get; </h4>
|
|
<div class="content">Gets the mode of the distribution.
|
|
|
|
</div>
|
|
</div>
|
|
<div id="N" class="method">
|
|
<h4><span title="System.int">int</span> <strong>N</strong> get; </h4>
|
|
<div class="content">Gets or sets the n parameter of the distribution.
|
|
|
|
</div>
|
|
</div>
|
|
<div id="RandomSource" class="method">
|
|
<h4><span title="System.Random">Random</span> <strong>RandomSource</strong> get; set;</h4>
|
|
<div class="content">Gets or sets the random number generator which is used to draw random samples.
|
|
|
|
</div>
|
|
</div>
|
|
<div id="S" class="method">
|
|
<h4><span title="System.double">double</span> <strong>S</strong> get; </h4>
|
|
<div class="content">Gets or sets the s parameter of the distribution.
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Skewness" class="method">
|
|
<h4><span title="System.double">double</span> <strong>Skewness</strong> get; </h4>
|
|
<div class="content">Gets the skewness of the distribution.
|
|
|
|
</div>
|
|
</div>
|
|
<div id="StdDev" class="method">
|
|
<h4><span title="System.double">double</span> <strong>StdDev</strong> get; </h4>
|
|
<div class="content">Gets the standard deviation of the distribution.
|
|
|
|
</div>
|
|
</div>
|
|
<div id="Variance" class="method">
|
|
<h4><span title="System.double">double</span> <strong>Variance</strong> get; </h4>
|
|
<div class="content">Gets the variance of the distribution.
|
|
|
|
</div>
|
|
</div>
|
|
<div id="footer">
|
|
<p>Based on v5.0.0.0 of MathNet.Numerics (Math.NET Numerics)</p>
|
|
<p>Generated by <a href="http://docu.jagregory.com">docu</a></p>
|
|
</div>
|
|
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|
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|