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 <div class="subTitle">org.apache.commons.math3.distribution</div>
 <h2 title="Class ZipfDistribution" class="title">Class ZipfDistribution</h2>
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 <li><a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html" title="class in org.apache.commons.math3.distribution">org.apache.commons.math3.distribution.AbstractIntegerDistribution</a></li>
 <li>
 <ul class="inheritance">
 <li>org.apache.commons.math3.distribution.ZipfDistribution</li>
 </ul>
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 </dl>
 <hr>
 <br>
 <pre>public class <span class="strong">ZipfDistribution</span>
 extends <a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractIntegerDistribution</a></pre>
 <div class="block">Implementation of the Zipf distribution.</div>
 <dl><dt><span class="strong">Version:</span></dt>
   <dd>$Id: ZipfDistribution.java 1533974 2013-10-20 20:42:41Z psteitz $</dd>
 <dt><span class="strong">See Also:</span></dt><dd><a href="http://mathworld.wolfram.com/ZipfDistribution.html">Zipf distribution (MathWorld)</a>,
 <a href="../../../../../serialized-form.html#org.apache.commons.math3.distribution.ZipfDistribution">Serialized Form</a></dd></dl>
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 <code><a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html#random">random</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html#randomData">randomData</a></code></li>
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 <th class="colOne" scope="col">Constructor and Description</th>
 </tr>
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 <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html#ZipfDistribution(int, double)">ZipfDistribution</a></strong>(int&nbsp;numberOfElements,
                 double&nbsp;exponent)</code>
 <div class="block">Create a new Zipf distribution with the given number of elements and
  exponent.</div>
 </td>
 </tr>
 <tr class="rowColor">
 <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html#ZipfDistribution(org.apache.commons.math3.random.RandomGenerator, int, double)">ZipfDistribution</a></strong>(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</a>&nbsp;rng,
                 int&nbsp;numberOfElements,
                 double&nbsp;exponent)</code>
 <div class="block">Creates a Zipf distribution.</div>
 </td>
 </tr>
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 <tr>
 <th class="colFirst" scope="col">Modifier and Type</th>
 <th class="colLast" scope="col">Method and Description</th>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>protected double</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html#calculateNumericalMean()">calculateNumericalMean</a></strong>()</code>
 <div class="block">Used by <a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html#getNumericalMean()"><code>getNumericalMean()</code></a>.</div>
 </td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>protected double</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html#calculateNumericalVariance()">calculateNumericalVariance</a></strong>()</code>
 <div class="block">Used by <a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html#getNumericalVariance()"><code>getNumericalVariance()</code></a>.</div>
 </td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>double</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html#cumulativeProbability(int)">cumulativeProbability</a></strong>(int&nbsp;x)</code>
 <div class="block">For a random variable <code>X</code> whose values are distributed according
  to this distribution, this method returns <code>P(X &lt;= x)</code>.</div>
 </td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>double</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html#getExponent()">getExponent</a></strong>()</code>
 <div class="block">Get the exponent characterizing the distribution.</div>
 </td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>int</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html#getNumberOfElements()">getNumberOfElements</a></strong>()</code>
 <div class="block">Get the number of elements (e.g.</div>
 </td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>double</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html#getNumericalMean()">getNumericalMean</a></strong>()</code>
 <div class="block">Use this method to get the numerical value of the mean of this
  distribution.</div>
 </td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>double</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html#getNumericalVariance()">getNumericalVariance</a></strong>()</code>
 <div class="block">Use this method to get the numerical value of the variance of this
  distribution.</div>
 </td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>int</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html#getSupportLowerBound()">getSupportLowerBound</a></strong>()</code>
 <div class="block">Access the lower bound of the support.</div>
 </td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>int</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html#getSupportUpperBound()">getSupportUpperBound</a></strong>()</code>
 <div class="block">Access the upper bound of the support.</div>
 </td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>boolean</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html#isSupportConnected()">isSupportConnected</a></strong>()</code>
 <div class="block">Use this method to get information about whether the support is
  connected, i.e.</div>
 </td>
 </tr>
 <tr class="altColor">
 <td class="colFirst"><code>double</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html#logProbability(int)">logProbability</a></strong>(int&nbsp;x)</code>
 <div class="block">For a random variable <code>X</code> whose values are distributed according to
  this distribution, this method returns <code>log(P(X = x))</code>, where
  <code>log</code> is the natural logarithm.</div>
 </td>
 </tr>
 <tr class="rowColor">
 <td class="colFirst"><code>double</code></td>
 <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html#probability(int)">probability</a></strong>(int&nbsp;x)</code>
 <div class="block">For a random variable <code>X</code> whose values are distributed according
  to this distribution, this method returns <code>P(X = x)</code>.</div>
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 <code><a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html#cumulativeProbability(int, int)">cumulativeProbability</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html#inverseCumulativeProbability(double)">inverseCumulativeProbability</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html#reseedRandomGenerator(long)">reseedRandomGenerator</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html#sample()">sample</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html#sample(int)">sample</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html#solveInverseCumulativeProbability(double, int, int)">solveInverseCumulativeProbability</a></code></li>
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 <h4>ZipfDistribution</h4>
 <pre>public&nbsp;ZipfDistribution(int&nbsp;numberOfElements,
                 double&nbsp;exponent)</pre>
 <div class="block">Create a new Zipf distribution with the given number of elements and
  exponent.</div>
 <dl><dt><span class="strong">Parameters:</span></dt><dd><code>numberOfElements</code> - Number of elements.</dd><dd><code>exponent</code> - Exponent.</dd>
 <dt><span class="strong">Throws:</span></dt>
 <dd><code><a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></code> - if <code>numberOfElements &lt;= 0</code>
  or <code>exponent &lt;= 0</code>.</dd></dl>
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 <h4>ZipfDistribution</h4>
 <pre>public&nbsp;ZipfDistribution(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</a>&nbsp;rng,
                 int&nbsp;numberOfElements,
                 double&nbsp;exponent)
                  throws <a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></pre>
 <div class="block">Creates a Zipf distribution.</div>
 <dl><dt><span class="strong">Parameters:</span></dt><dd><code>rng</code> - Random number generator.</dd><dd><code>numberOfElements</code> - Number of elements.</dd><dd><code>exponent</code> - Exponent.</dd>
 <dt><span class="strong">Throws:</span></dt>
 <dd><code><a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></code> - if <code>numberOfElements &lt;= 0</code>
  or <code>exponent &lt;= 0</code>.</dd><dt><span class="strong">Since:</span></dt>
   <dd>3.1</dd></dl>
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 <pre>public&nbsp;int&nbsp;getNumberOfElements()</pre>
 <div class="block">Get the number of elements (e.g. corpus size) for the distribution.</div>
 <dl><dt><span class="strong">Returns:</span></dt><dd>the number of elements</dd></dl>
 </li>
 </ul>
 <a name="getExponent()">
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 <h4>getExponent</h4>
 <pre>public&nbsp;double&nbsp;getExponent()</pre>
 <div class="block">Get the exponent characterizing the distribution.</div>
 <dl><dt><span class="strong">Returns:</span></dt><dd>the exponent</dd></dl>
 </li>
 </ul>
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 <h4>probability</h4>
 <pre>public&nbsp;double&nbsp;probability(int&nbsp;x)</pre>
 <div class="block">For a random variable <code>X</code> whose values are distributed according
  to this distribution, this method returns <code>P(X = x)</code>. In other
  words, this method represents the probability mass function (PMF)
  for the distribution.</div>
 <dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the point at which the PMF is evaluated</dd>
 <dt><span class="strong">Returns:</span></dt><dd>the value of the probability mass function at <code>x</code></dd></dl>
 </li>
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 <pre>public&nbsp;double&nbsp;logProbability(int&nbsp;x)</pre>
 <div class="block">For a random variable <code>X</code> whose values are distributed according to
  this distribution, this method returns <code>log(P(X = x))</code>, where
  <code>log</code> is the natural logarithm. In other words, this method
  represents the logarithm of the probability mass function (PMF) for the
  distribution. Note that due to the floating point precision and
  under/overflow issues, this method will for some distributions be more
  precise and faster than computing the logarithm of
  <a href="../../../../../org/apache/commons/math3/distribution/IntegerDistribution.html#probability(int)"><code>IntegerDistribution.probability(int)</code></a>.
  <p>
  The default implementation simply computes the logarithm of <code>probability(x)</code>.</p></div>
 <dl>
 <dt><strong>Overrides:</strong></dt>
 <dd><code><a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html#logProbability(int)">logProbability</a></code>&nbsp;in class&nbsp;<code><a href="../../../../../org/apache/commons/math3/distribution/AbstractIntegerDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractIntegerDistribution</a></code></dd>
 <dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the point at which the PMF is evaluated</dd>
 <dt><span class="strong">Returns:</span></dt><dd>the logarithm of the value of the probability mass function at <code>x</code></dd></dl>
 </li>
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 <pre>public&nbsp;double&nbsp;cumulativeProbability(int&nbsp;x)</pre>
 <div class="block">For a random variable <code>X</code> whose values are distributed according
  to this distribution, this method returns <code>P(X &lt;= x)</code>.  In other
  words, this method represents the (cumulative) distribution function
  (CDF) for this distribution.</div>
 <dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the point at which the CDF is evaluated</dd>
 <dt><span class="strong">Returns:</span></dt><dd>the probability that a random variable with this
  distribution takes a value less than or equal to <code>x</code></dd></dl>
 </li>
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 <pre>public&nbsp;double&nbsp;getNumericalMean()</pre>
 <div class="block">Use this method to get the numerical value of the mean of this
  distribution.

  For number of elements <code>N</code> and exponent <code>s</code>, the mean is
  <code>Hs1 / Hs</code>, where
  <ul>
   <li><code>Hs1 = generalizedHarmonic(N, s - 1)</code>,</li>
   <li><code>Hs = generalizedHarmonic(N, s)</code>.</li>
  </ul></div>
 <dl><dt><span class="strong">Returns:</span></dt><dd>the mean or <code>Double.NaN</code> if it is not defined</dd></dl>
 </li>
 </ul>
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 <pre>protected&nbsp;double&nbsp;calculateNumericalMean()</pre>
 <div class="block">Used by <a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html#getNumericalMean()"><code>getNumericalMean()</code></a>.</div>
 <dl><dt><span class="strong">Returns:</span></dt><dd>the mean of this distribution</dd></dl>
 </li>
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 <pre>public&nbsp;double&nbsp;getNumericalVariance()</pre>
 <div class="block">Use this method to get the numerical value of the variance of this
  distribution.

  For number of elements <code>N</code> and exponent <code>s</code>, the mean is
  <code>(Hs2 / Hs) - (Hs1^2 / Hs^2)</code>, where
  <ul>
   <li><code>Hs2 = generalizedHarmonic(N, s - 2)</code>,</li>
   <li><code>Hs1 = generalizedHarmonic(N, s - 1)</code>,</li>
   <li><code>Hs = generalizedHarmonic(N, s)</code>.</li>
  </ul></div>
 <dl><dt><span class="strong">Returns:</span></dt><dd>the variance (possibly <code>Double.POSITIVE_INFINITY</code> or
  <code>Double.NaN</code> if it is not defined)</dd></dl>
 </li>
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 <h4>calculateNumericalVariance</h4>
 <pre>protected&nbsp;double&nbsp;calculateNumericalVariance()</pre>
 <div class="block">Used by <a href="../../../../../org/apache/commons/math3/distribution/ZipfDistribution.html#getNumericalVariance()"><code>getNumericalVariance()</code></a>.</div>
 <dl><dt><span class="strong">Returns:</span></dt><dd>the variance of this distribution</dd></dl>
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 <h4>getSupportLowerBound</h4>
 <pre>public&nbsp;int&nbsp;getSupportLowerBound()</pre>
 <div class="block">Access the lower bound of the support. This method must return the same
  value as <code>inverseCumulativeProbability(0)</code>. In other words, this
  method must return
  <p><code>inf {x in Z | P(X <= x) > 0}</code>.</p>

  The lower bound of the support is always 1 no matter the parameters.</div>
 <dl><dt><span class="strong">Returns:</span></dt><dd>lower bound of the support (always 1)</dd></dl>
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 <h4>getSupportUpperBound</h4>
 <pre>public&nbsp;int&nbsp;getSupportUpperBound()</pre>
 <div class="block">Access the upper bound of the support. This method must return the same
  value as <code>inverseCumulativeProbability(1)</code>. In other words, this
  method must return
  <p><code>inf {x in R | P(X <= x) = 1}</code>.</p>

  The upper bound of the support is the number of elements.</div>
 <dl><dt><span class="strong">Returns:</span></dt><dd>upper bound of the support</dd></dl>
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 <h4>isSupportConnected</h4>
 <pre>public&nbsp;boolean&nbsp;isSupportConnected()</pre>
 <div class="block">Use this method to get information about whether the support is
  connected, i.e. whether all integers between the lower and upper bound of
  the support are included in the support.

  The support of this distribution is connected.</div>
 <dl><dt><span class="strong">Returns:</span></dt><dd><code>true</code></dd></dl>
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