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| <h2 title="Class KolmogorovSmirnovDistribution" class="title">Class KolmogorovSmirnovDistribution</h2> |
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| <li>org.apache.commons.math3.distribution.KolmogorovSmirnovDistribution</li> |
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| </dl> |
| <hr> |
| <div class="block"><strong>Deprecated.</strong> |
| <div class="block"><i>to be removed in version 4.0 - |
| use <a href="../../../../../org/apache/commons/math3/stat/inference/KolmogorovSmirnovTest.html" title="class in org.apache.commons.math3.stat.inference"><code>KolmogorovSmirnovTest</code></a></i></div> |
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| <pre>public class <span class="strong">KolmogorovSmirnovDistribution</span> |
| extends <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a> |
| implements <a href="http://docs.oracle.com/javase/6/docs/api/java/io/Serializable.html?is-external=true" title="class or interface in java.io">Serializable</a></pre> |
| <div class="block">Implementation of the Kolmogorov-Smirnov distribution. |
| |
| <p> |
| Treats the distribution of the two-sided <code>P(D_n < d)</code> where |
| <code>D_n = sup_x |G(x) - G_n (x)|</code> for the theoretical cdf <code>G</code> and |
| the empirical cdf <code>G_n</code>. |
| </p> |
| <p> |
| This implementation is based on [1] with certain quick decisions for extreme |
| values given in [2]. |
| </p> |
| <p> |
| In short, when wanting to evaluate <code>P(D_n < d)</code>, the method in [1] is |
| to write <code>d = (k - h) / n</code> for positive integer <code>k</code> and |
| <code>0 <= h < 1</code>. Then <code>P(D_n < d) = (n! / n^n) * t_kk</code>, where |
| <code>t_kk</code> is the <code>(k, k)</code>'th entry in the special matrix |
| <code>H^n</code>, i.e. <code>H</code> to the <code>n</code>'th power. |
| </p> |
| <p> |
| References: |
| <ul> |
| <li>[1] <a href="http://www.jstatsoft.org/v08/i18/"> |
| Evaluating Kolmogorov's Distribution</a> by George Marsaglia, Wai |
| Wan Tsang, and Jingbo Wang</li> |
| <li>[2] <a href="http://www.jstatsoft.org/v39/i11/"> |
| Computing the Two-Sided Kolmogorov-Smirnov Distribution</a> by Richard Simard |
| and Pierre L'Ecuyer</li> |
| </ul> |
| Note that [1] contains an error in computing h, refer to |
| <a href="https://issues.apache.org/jira/browse/MATH-437">MATH-437</a> for details. |
| </p></div> |
| <dl><dt><span class="strong">Version:</span></dt> |
| <dd>$Id: KolmogorovSmirnovDistribution.java 1591211 2014-04-30 08:20:51Z luc $</dd> |
| <dt><span class="strong">See Also:</span></dt><dd><a href="http://en.wikipedia.org/wiki/Kolmogorov-Smirnov_test"> |
| Kolmogorov-Smirnov test (Wikipedia)</a>, |
| <a href="../../../../../serialized-form.html#org.apache.commons.math3.distribution.KolmogorovSmirnovDistribution">Serialized Form</a></dd></dl> |
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| <td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/KolmogorovSmirnovDistribution.html#KolmogorovSmirnovDistribution(int)">KolmogorovSmirnovDistribution</a></strong>(int n)</code> |
| <div class="block"><strong>Deprecated.</strong> </div> |
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| <td class="colFirst"><code>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/distribution/KolmogorovSmirnovDistribution.html#cdf(double)">cdf</a></strong>(double d)</code> |
| <div class="block"><strong>Deprecated.</strong> </div> |
| <div class="block">Calculates <code>P(D_n < d)</code> using method described in [1] with quick |
| decisions for extreme values given in [2] (see above).</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/KolmogorovSmirnovDistribution.html#cdf(double, boolean)">cdf</a></strong>(double d, |
| boolean exact)</code> |
| <div class="block"><strong>Deprecated.</strong> </div> |
| <div class="block">Calculates <code>P(D_n < d)</code> using method described in [1] with quick |
| decisions for extreme values given in [2] (see above).</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/KolmogorovSmirnovDistribution.html#cdfExact(double)">cdfExact</a></strong>(double d)</code> |
| <div class="block"><strong>Deprecated.</strong> </div> |
| <div class="block">Calculates <code>P(D_n < d)</code> using method described in [1] with quick |
| decisions for extreme values given in [2] (see above).</div> |
| </td> |
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| <h4>KolmogorovSmirnovDistribution</h4> |
| <pre>public KolmogorovSmirnovDistribution(int n) |
| throws <a href="../../../../../org/apache/commons/math3/exception/NotStrictlyPositiveException.html" title="class in org.apache.commons.math3.exception">NotStrictlyPositiveException</a></pre> |
| <div class="block"><span class="strong">Deprecated.</span> </div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>n</code> - Number of observations</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>n <= 0</code></dd></dl> |
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| <h4>cdf</h4> |
| <pre>public double cdf(double d) |
| throws <a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></pre> |
| <div class="block"><span class="strong">Deprecated.</span> </div> |
| <div class="block">Calculates <code>P(D_n < d)</code> using method described in [1] with quick |
| decisions for extreme values given in [2] (see above). The result is not |
| exact as with |
| <a href="../../../../../org/apache/commons/math3/distribution/KolmogorovSmirnovDistribution.html#cdfExact(double)"><code>cdfExact(double)</code></a> because |
| calculations are based on <code>double</code> rather than |
| <a href="../../../../../org/apache/commons/math3/fraction/BigFraction.html" title="class in org.apache.commons.math3.fraction"><code>BigFraction</code></a>.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>d</code> - statistic</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the two-sided probability of <code>P(D_n < d)</code></dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></code> - if algorithm fails to convert <code>h</code> |
| to a <a href="../../../../../org/apache/commons/math3/fraction/BigFraction.html" title="class in org.apache.commons.math3.fraction"><code>BigFraction</code></a> in expressing |
| <code>d</code> as <code>(k - h) / m</code> for integer <code>k, m</code> and |
| <code>0 <= h < 1</code>.</dd></dl> |
| </li> |
| </ul> |
| <a name="cdfExact(double)"> |
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| <h4>cdfExact</h4> |
| <pre>public double cdfExact(double d) |
| throws <a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></pre> |
| <div class="block"><span class="strong">Deprecated.</span> </div> |
| <div class="block">Calculates <code>P(D_n < d)</code> using method described in [1] with quick |
| decisions for extreme values given in [2] (see above). The result is |
| exact in the sense that BigFraction/BigReal is used everywhere at the |
| expense of very slow execution time. Almost never choose this in real |
| applications unless you are very sure; this is almost solely for |
| verification purposes. Normally, you would choose |
| <a href="../../../../../org/apache/commons/math3/distribution/KolmogorovSmirnovDistribution.html#cdf(double)"><code>cdf(double)</code></a></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>d</code> - statistic</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the two-sided probability of <code>P(D_n < d)</code></dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></code> - if algorithm fails to convert <code>h</code> |
| to a <a href="../../../../../org/apache/commons/math3/fraction/BigFraction.html" title="class in org.apache.commons.math3.fraction"><code>BigFraction</code></a> in expressing |
| <code>d</code> as <code>(k - h) / m</code> for integer <code>k, m</code> and |
| <code>0 <= h < 1</code>.</dd></dl> |
| </li> |
| </ul> |
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| <h4>cdf</h4> |
| <pre>public double cdf(double d, |
| boolean exact) |
| throws <a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></pre> |
| <div class="block"><span class="strong">Deprecated.</span> </div> |
| <div class="block">Calculates <code>P(D_n < d)</code> using method described in [1] with quick |
| decisions for extreme values given in [2] (see above).</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>d</code> - statistic</dd><dd><code>exact</code> - whether the probability should be calculated exact using |
| <a href="../../../../../org/apache/commons/math3/fraction/BigFraction.html" title="class in org.apache.commons.math3.fraction"><code>BigFraction</code></a> everywhere at the |
| expense of very slow execution time, or if <code>double</code> should be used |
| convenient places to gain speed. Almost never choose <code>true</code> in real |
| applications unless you are very sure; <code>true</code> is almost solely for |
| verification purposes.</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>the two-sided probability of <code>P(D_n < d)</code></dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></code> - if algorithm fails to convert <code>h</code> |
| to a <a href="../../../../../org/apache/commons/math3/fraction/BigFraction.html" title="class in org.apache.commons.math3.fraction"><code>BigFraction</code></a> in expressing |
| <code>d</code> as <code>(k - h) / m</code> for integer <code>k, m</code> and |
| <code>0 <= h < 1</code>.</dd></dl> |
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