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<h2 title="Class KolmogorovSmirnovDistribution" class="title">Class KolmogorovSmirnovDistribution</h2>
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<div class="block"><strong>Deprecated.</strong>&nbsp;
<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 &lt; 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 &lt; d)</code>, the method in [1] is
to write <code>d = (k - h) / n</code> for positive integer <code>k</code> and
<code>0 &lt;= h &lt; 1</code>. Then <code>P(D_n &lt; 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&nbsp;n)</code>
<div class="block"><strong>Deprecated.</strong>&nbsp;</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&nbsp;d)</code>
<div class="block"><strong>Deprecated.</strong>&nbsp;</div>
<div class="block">Calculates <code>P(D_n &lt; 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&nbsp;d,
boolean&nbsp;exact)</code>
<div class="block"><strong>Deprecated.</strong>&nbsp;</div>
<div class="block">Calculates <code>P(D_n &lt; 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&nbsp;d)</code>
<div class="block"><strong>Deprecated.</strong>&nbsp;</div>
<div class="block">Calculates <code>P(D_n &lt; d)</code> using method described in [1] with quick
decisions for extreme values given in [2] (see above).</div>
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<h4>KolmogorovSmirnovDistribution</h4>
<pre>public&nbsp;KolmogorovSmirnovDistribution(int&nbsp;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>&nbsp;</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 &lt;= 0</code></dd></dl>
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<h4>cdf</h4>
<pre>public&nbsp;double&nbsp;cdf(double&nbsp;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>&nbsp;</div>
<div class="block">Calculates <code>P(D_n &lt; 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 &lt; 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 &lt;= h &lt; 1</code>.</dd></dl>
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<h4>cdfExact</h4>
<pre>public&nbsp;double&nbsp;cdfExact(double&nbsp;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>&nbsp;</div>
<div class="block">Calculates <code>P(D_n &lt; 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 &lt; 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 &lt;= h &lt; 1</code>.</dd></dl>
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<h4>cdf</h4>
<pre>public&nbsp;double&nbsp;cdf(double&nbsp;d,
boolean&nbsp;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>&nbsp;</div>
<div class="block">Calculates <code>P(D_n &lt; 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 &lt; 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 &lt;= h &lt; 1</code>.</dd></dl>
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