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| <div class="subTitle">org.apache.commons.math3.distribution</div> |
| <h2 title="Class ParetoDistribution" class="title">Class ParetoDistribution</h2> |
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| <li><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">org.apache.commons.math3.distribution.AbstractRealDistribution</a></li> |
| <li> |
| <ul class="inheritance"> |
| <li>org.apache.commons.math3.distribution.ParetoDistribution</li> |
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| <pre>public class <span class="strong">ParetoDistribution</span> |
| extends <a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</a></pre> |
| <div class="block">Implementation of the Pareto distribution. |
| |
| <p> |
| <strong>Parameters:</strong> |
| The probability distribution function of <code>X</code> is given by (for <code>x >= k</code>): |
| <pre> |
| α * k^α / x^(α + 1) |
| </pre> |
| <p> |
| <ul> |
| <li><code>k</code> is the <em>scale</em> parameter: this is the minimum possible value of <code>X</code>,</li> |
| <li><code>α</code> is the <em>shape</em> parameter: this is the Pareto index</li> |
| </ul></div> |
| <dl><dt><span class="strong">Since:</span></dt> |
| <dd>3.3</dd> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: ParetoDistribution.java 1533974 2013-10-20 20:42:41Z psteitz $</dd> |
| <dt><span class="strong">See Also:</span></dt><dd><a href="http://en.wikipedia.org/wiki/Pareto_distribution"> |
| Pareto distribution (Wikipedia)</a>, |
| <a href="http://mathworld.wolfram.com/ParetoDistribution.html"> |
| Pareto distribution (MathWorld)</a>, |
| <a href="../../../../../serialized-form.html#org.apache.commons.math3.distribution.ParetoDistribution">Serialized Form</a></dd></dl> |
| </li> |
| </ul> |
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| <td class="colFirst"><code>static double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ParetoDistribution.html#DEFAULT_INVERSE_ABSOLUTE_ACCURACY">DEFAULT_INVERSE_ABSOLUTE_ACCURACY</a></strong></code> |
| <div class="block">Default inverse cumulative probability accuracy.</div> |
| </td> |
| </tr> |
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| <h3>Fields inherited from class org.apache.commons.math3.distribution.<a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</a></h3> |
| <code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#random">random</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#randomData">randomData</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#SOLVER_DEFAULT_ABSOLUTE_ACCURACY">SOLVER_DEFAULT_ABSOLUTE_ACCURACY</a></code></li> |
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| <th class="colOne" scope="col">Constructor and Description</th> |
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| <tr class="altColor"> |
| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ParetoDistribution.html#ParetoDistribution()">ParetoDistribution</a></strong>()</code> |
| <div class="block">Create a Pareto distribution with a scale of <code>1</code> and a shape of <code>1</code>.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ParetoDistribution.html#ParetoDistribution(double, double)">ParetoDistribution</a></strong>(double scale, |
| double shape)</code> |
| <div class="block">Create a Pareto distribution using the specified scale and shape.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ParetoDistribution.html#ParetoDistribution(double, double, double)">ParetoDistribution</a></strong>(double scale, |
| double shape, |
| double inverseCumAccuracy)</code> |
| <div class="block">Create a Pareto distribution using the specified scale, shape and |
| inverse cumulative distribution accuracy.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ParetoDistribution.html#ParetoDistribution(org.apache.commons.math3.random.RandomGenerator, double, double)">ParetoDistribution</a></strong>(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</a> rng, |
| double scale, |
| double shape)</code> |
| <div class="block">Creates a log-normal distribution.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ParetoDistribution.html#ParetoDistribution(org.apache.commons.math3.random.RandomGenerator, double, double, double)">ParetoDistribution</a></strong>(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</a> rng, |
| double scale, |
| double shape, |
| double inverseCumAccuracy)</code> |
| <div class="block">Creates a log-normal distribution.</div> |
| </td> |
| </tr> |
| </table> |
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| <caption><span>Methods</span><span class="tabEnd"> </span></caption> |
| <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>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ParetoDistribution.html#cumulativeProbability(double)">cumulativeProbability</a></strong>(double 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> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ParetoDistribution.html#cumulativeProbability(double, double)">cumulativeProbability</a></strong>(double x0, |
| double x1)</code> |
| <div class="block"><strong>Deprecated.</strong> |
| <div class="block"><i>See <a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#cumulativeProbability(double, double)"><code>RealDistribution.cumulativeProbability(double,double)</code></a></i></div> |
| </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/ParetoDistribution.html#density(double)">density</a></strong>(double x)</code> |
| <div class="block">Returns the probability density function (PDF) of this distribution |
| evaluated at the specified point <code>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/ParetoDistribution.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/ParetoDistribution.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>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ParetoDistribution.html#getScale()">getScale</a></strong>()</code> |
| <div class="block">Returns the scale parameter 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/ParetoDistribution.html#getShape()">getShape</a></strong>()</code> |
| <div class="block">Returns the shape parameter of this distribution.</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/ParetoDistribution.html#getSolverAbsoluteAccuracy()">getSolverAbsoluteAccuracy</a></strong>()</code> |
| <div class="block">Returns the solver absolute accuracy for inverse cumulative computation.</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/ParetoDistribution.html#getSupportLowerBound()">getSupportLowerBound</a></strong>()</code> |
| <div class="block">Access the lower bound of the support.</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/ParetoDistribution.html#getSupportUpperBound()">getSupportUpperBound</a></strong>()</code> |
| <div class="block">Access the upper bound of the support.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>boolean</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ParetoDistribution.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="rowColor"> |
| <td class="colFirst"><code>boolean</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ParetoDistribution.html#isSupportLowerBoundInclusive()">isSupportLowerBoundInclusive</a></strong>()</code> |
| <div class="block">Whether or not the lower bound of support is in the domain of the density |
| function.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>boolean</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/ParetoDistribution.html#isSupportUpperBoundInclusive()">isSupportUpperBoundInclusive</a></strong>()</code> |
| <div class="block">Whether or not the upper bound of support is in the domain of the density |
| function.</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/ParetoDistribution.html#logDensity(double)">logDensity</a></strong>(double x)</code> |
| <div class="block">Returns the natural logarithm of the probability density function (PDF) of this distribution |
| evaluated at the specified point <code>x</code>.</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/ParetoDistribution.html#sample()">sample</a></strong>()</code> |
| <div class="block">Generate a random value sampled from this distribution.</div> |
| </td> |
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| <h3>Methods inherited from class org.apache.commons.math3.distribution.<a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</a></h3> |
| <code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#inverseCumulativeProbability(double)">inverseCumulativeProbability</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#probability(double)">probability</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#probability(double, double)">probability</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#reseedRandomGenerator(long)">reseedRandomGenerator</a>, <a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#sample(int)">sample</a></code></li> |
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| <h4>DEFAULT_INVERSE_ABSOLUTE_ACCURACY</h4> |
| <pre>public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY</pre> |
| <div class="block">Default inverse cumulative probability accuracy.</div> |
| <dl><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../constant-values.html#org.apache.commons.math3.distribution.ParetoDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY">Constant Field Values</a></dd></dl> |
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| <h4>ParetoDistribution</h4> |
| <pre>public ParetoDistribution()</pre> |
| <div class="block">Create a Pareto distribution with a scale of <code>1</code> and a shape of <code>1</code>.</div> |
| </li> |
| </ul> |
| <a name="ParetoDistribution(double, double)"> |
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| <h4>ParetoDistribution</h4> |
| <pre>public ParetoDistribution(double scale, |
| double shape) |
| throws <a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></pre> |
| <div class="block">Create a Pareto distribution using the specified scale and shape.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>scale</code> - the scale parameter of this distribution</dd><dd><code>shape</code> - the shape parameter of this distribution</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>scale <= 0</code> or <code>shape <= 0</code>.</dd></dl> |
| </li> |
| </ul> |
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| <h4>ParetoDistribution</h4> |
| <pre>public ParetoDistribution(double scale, |
| double shape, |
| double inverseCumAccuracy) |
| throws <a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></pre> |
| <div class="block">Create a Pareto distribution using the specified scale, shape and |
| inverse cumulative distribution accuracy.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>scale</code> - the scale parameter of this distribution</dd><dd><code>shape</code> - the shape parameter of this distribution</dd><dd><code>inverseCumAccuracy</code> - Inverse cumulative probability accuracy.</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>scale <= 0</code> or <code>shape <= 0</code>.</dd></dl> |
| </li> |
| </ul> |
| <a name="ParetoDistribution(org.apache.commons.math3.random.RandomGenerator, double, double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
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| <h4>ParetoDistribution</h4> |
| <pre>public ParetoDistribution(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</a> rng, |
| double scale, |
| double shape) |
| 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 log-normal distribution.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>rng</code> - Random number generator.</dd><dd><code>scale</code> - Scale parameter of this distribution.</dd><dd><code>shape</code> - Shape parameter of this distribution.</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>scale <= 0</code> or <code>shape <= 0</code>.</dd></dl> |
| </li> |
| </ul> |
| <a name="ParetoDistribution(org.apache.commons.math3.random.RandomGenerator, double, double, double)"> |
| <!-- --> |
| </a> |
| <ul class="blockListLast"> |
| <li class="blockList"> |
| <h4>ParetoDistribution</h4> |
| <pre>public ParetoDistribution(<a href="../../../../../org/apache/commons/math3/random/RandomGenerator.html" title="interface in org.apache.commons.math3.random">RandomGenerator</a> rng, |
| double scale, |
| double shape, |
| double inverseCumAccuracy) |
| 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 log-normal distribution.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>rng</code> - Random number generator.</dd><dd><code>scale</code> - Scale parameter of this distribution.</dd><dd><code>shape</code> - Shape parameter of this distribution.</dd><dd><code>inverseCumAccuracy</code> - Inverse cumulative probability accuracy.</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>scale <= 0</code> or <code>shape <= 0</code>.</dd></dl> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| <!-- ============ METHOD DETAIL ========== --> |
| <ul class="blockList"> |
| <li class="blockList"><a name="method_detail"> |
| <!-- --> |
| </a> |
| <h3>Method Detail</h3> |
| <a name="getScale()"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>getScale</h4> |
| <pre>public double getScale()</pre> |
| <div class="block">Returns the scale parameter of this distribution.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>the scale parameter</dd></dl> |
| </li> |
| </ul> |
| <a name="getShape()"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>getShape</h4> |
| <pre>public double getShape()</pre> |
| <div class="block">Returns the shape parameter of this distribution.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>the shape parameter</dd></dl> |
| </li> |
| </ul> |
| <a name="density(double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>density</h4> |
| <pre>public double density(double x)</pre> |
| <div class="block">Returns the probability density function (PDF) of this distribution |
| evaluated at the specified point <code>x</code>. In general, the PDF is |
| the derivative of the <a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#cumulativeProbability(double)"><code>CDF</code></a>. |
| If the derivative does not exist at <code>x</code>, then an appropriate |
| replacement should be returned, e.g. <code>Double.POSITIVE_INFINITY</code>, |
| <code>Double.NaN</code>, or the limit inferior or limit superior of the |
| difference quotient. |
| <p> |
| For scale <code>k</code>, and shape <code>α</code> of this distribution, the PDF |
| is given by |
| <ul> |
| <li><code>0</code> if <code>x < k</code>,</li> |
| <li><code>α * k^α / x^(α + 1)</code> otherwise.</li> |
| </ul></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the point at which the PDF is evaluated</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the value of the probability density function at point <code>x</code></dd></dl> |
| </li> |
| </ul> |
| <a name="logDensity(double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>logDensity</h4> |
| <pre>public double logDensity(double x)</pre> |
| <div class="block">Returns the natural logarithm of the probability density function (PDF) of this distribution |
| evaluated at the specified point <code>x</code>. In general, the PDF is the derivative of the |
| <a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#cumulativeProbability(double)"><code>CDF</code></a>. If the derivative does not exist at <code>x</code>, |
| then an appropriate replacement should be returned, e.g. <code>Double.POSITIVE_INFINITY</code>, |
| <code>Double.NaN</code>, or the limit inferior or limit superior of the difference quotient. 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/RealDistribution.html#density(double)"><code>RealDistribution.density(double)</code></a>. The default implementation simply computes the logarithm of |
| <code>density(x)</code>. |
| |
| See documentation of <a href="../../../../../org/apache/commons/math3/distribution/ParetoDistribution.html#density(double)"><code>density(double)</code></a> for computation details.</div> |
| <dl> |
| <dt><strong>Overrides:</strong></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#logDensity(double)">logDensity</a></code> in class <code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</a></code></dd> |
| <dt><span class="strong">Parameters:</span></dt><dd><code>x</code> - the point at which the PDF is evaluated</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the logarithm of the value of the probability density function at point <code>x</code></dd></dl> |
| </li> |
| </ul> |
| <a name="cumulativeProbability(double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>cumulativeProbability</h4> |
| <pre>public double cumulativeProbability(double 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 (cumulative) distribution function |
| (CDF) for this distribution. |
| <p> |
| For scale <code>k</code>, and shape <code>α</code> of this distribution, the CDF is given by |
| <ul> |
| <li><code>0</code> if <code>x < k</code>,</li> |
| <li><code>1 - (k / x)^α</code> otherwise.</li> |
| </ul></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> |
| </ul> |
| <a name="cumulativeProbability(double, double)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>cumulativeProbability</h4> |
| <pre><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Deprecated.html?is-external=true" title="class or interface in java.lang">@Deprecated</a> |
| public double cumulativeProbability(double x0, |
| double x1) |
| throws <a href="../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a></pre> |
| <div class="block"><span class="strong">Deprecated.</span> <i>See <a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#cumulativeProbability(double, double)"><code>RealDistribution.cumulativeProbability(double,double)</code></a></i></div> |
| <div class="block">For a random variable <code>X</code> whose values are distributed according |
| to this distribution, this method returns <code>P(x0 < X <= x1)</code>. |
| |
| The default implementation uses the identity |
| <p><code>P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)</code></p></div> |
| <dl> |
| <dt><strong>Specified by:</strong></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#cumulativeProbability(double, double)">cumulativeProbability</a></code> in interface <code><a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html" title="interface in org.apache.commons.math3.distribution">RealDistribution</a></code></dd> |
| <dt><strong>Overrides:</strong></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#cumulativeProbability(double, double)">cumulativeProbability</a></code> in class <code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</a></code></dd> |
| <dt><span class="strong">Parameters:</span></dt><dd><code>x0</code> - the exclusive lower bound</dd><dd><code>x1</code> - the inclusive upper bound</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the probability that a random variable with this distribution |
| takes a value between <code>x0</code> and <code>x1</code>, |
| excluding the lower and including the upper endpoint</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/NumberIsTooLargeException.html" title="class in org.apache.commons.math3.exception">NumberIsTooLargeException</a></code> - if <code>x0 > x1</code></dd></dl> |
| </li> |
| </ul> |
| <a name="getSolverAbsoluteAccuracy()"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>getSolverAbsoluteAccuracy</h4> |
| <pre>protected double getSolverAbsoluteAccuracy()</pre> |
| <div class="block">Returns the solver absolute accuracy for inverse cumulative computation. |
| You can override this method in order to use a Brent solver with an |
| absolute accuracy different from the default.</div> |
| <dl> |
| <dt><strong>Overrides:</strong></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#getSolverAbsoluteAccuracy()">getSolverAbsoluteAccuracy</a></code> in class <code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</a></code></dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the maximum absolute error in inverse cumulative probability estimates</dd></dl> |
| </li> |
| </ul> |
| <a name="getNumericalMean()"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>getNumericalMean</h4> |
| <pre>public double getNumericalMean()</pre> |
| <div class="block">Use this method to get the numerical value of the mean of this |
| distribution. |
| <p> |
| For scale <code>k</code> and shape <code>α</code>, the mean is given by |
| <ul> |
| <li><code>∞</code> if <code>α <= 1</code>,</li> |
| <li><code>α * k / (α - 1)</code> otherwise.</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> |
| <a name="getNumericalVariance()"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>getNumericalVariance</h4> |
| <pre>public double getNumericalVariance()</pre> |
| <div class="block">Use this method to get the numerical value of the variance of this |
| distribution. |
| <p> |
| For scale <code>k</code> and shape <code>α</code>, the variance is given by |
| <ul> |
| <li><code>∞</code> if <code>1 < α <= 2</code>,</li> |
| <li><code>k^2 * α / ((α - 1)^2 * (α - 2))</code> otherwise.</li> |
| </ul></div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>the variance (possibly <code>Double.POSITIVE_INFINITY</code> as |
| for certain cases in <a href="../../../../../org/apache/commons/math3/distribution/TDistribution.html" title="class in org.apache.commons.math3.distribution"><code>TDistribution</code></a>) or <code>Double.NaN</code> if it |
| is not defined</dd></dl> |
| </li> |
| </ul> |
| <a name="getSupportLowerBound()"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>getSupportLowerBound</h4> |
| <pre>public double 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 R | P(X <= x) > 0}</code>.</p> |
| <p> |
| The lower bound of the support is equal to the scale parameter <code>k</code>.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>lower bound of the support</dd></dl> |
| </li> |
| </ul> |
| <a name="getSupportUpperBound()"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>getSupportUpperBound</h4> |
| <pre>public double 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> |
| <p> |
| The upper bound of the support is always positive infinity no matter the parameters.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>upper bound of the support (always <code>Double.POSITIVE_INFINITY</code>)</dd></dl> |
| </li> |
| </ul> |
| <a name="isSupportLowerBoundInclusive()"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>isSupportLowerBoundInclusive</h4> |
| <pre>public boolean isSupportLowerBoundInclusive()</pre> |
| <div class="block">Whether or not the lower bound of support is in the domain of the density |
| function. Returns true iff <code>getSupporLowerBound()</code> is finite and |
| <code>density(getSupportLowerBound())</code> returns a non-NaN, non-infinite |
| value.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>true if the lower bound of support is finite and the density |
| function returns a non-NaN, non-infinite value there</dd></dl> |
| </li> |
| </ul> |
| <a name="isSupportUpperBoundInclusive()"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>isSupportUpperBoundInclusive</h4> |
| <pre>public boolean isSupportUpperBoundInclusive()</pre> |
| <div class="block">Whether or not the upper bound of support is in the domain of the density |
| function. Returns true iff <code>getSupportUpperBound()</code> is finite and |
| <code>density(getSupportUpperBound())</code> returns a non-NaN, non-infinite |
| value.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>true if the upper bound of support is finite and the density |
| function returns a non-NaN, non-infinite value there</dd></dl> |
| </li> |
| </ul> |
| <a name="isSupportConnected()"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>isSupportConnected</h4> |
| <pre>public boolean isSupportConnected()</pre> |
| <div class="block">Use this method to get information about whether the support is connected, |
| i.e. whether all values between the lower and upper bound of the support |
| are included in the support. |
| <p> |
| The support of this distribution is connected.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd><code>true</code></dd></dl> |
| </li> |
| </ul> |
| <a name="sample()"> |
| <!-- --> |
| </a> |
| <ul class="blockListLast"> |
| <li class="blockList"> |
| <h4>sample</h4> |
| <pre>public double sample()</pre> |
| <div class="block">Generate a random value sampled from this distribution. |
| |
| The default implementation uses the |
| <a href="http://en.wikipedia.org/wiki/Inverse_transform_sampling"> |
| inversion method. |
| </a></div> |
| <dl> |
| <dt><strong>Specified by:</strong></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html#sample()">sample</a></code> in interface <code><a href="../../../../../org/apache/commons/math3/distribution/RealDistribution.html" title="interface in org.apache.commons.math3.distribution">RealDistribution</a></code></dd> |
| <dt><strong>Overrides:</strong></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html#sample()">sample</a></code> in class <code><a href="../../../../../org/apache/commons/math3/distribution/AbstractRealDistribution.html" title="class in org.apache.commons.math3.distribution">AbstractRealDistribution</a></code></dd> |
| <dt><span class="strong">Returns:</span></dt><dd>a random value.</dd></dl> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| </li> |
| </ul> |
| </div> |
| </div> |
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