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| <div class="subTitle">org.apache.commons.math3.stat.correlation</div> |
| <h2 title="Class KendallsCorrelation" class="title">Class KendallsCorrelation</h2> |
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| <li>org.apache.commons.math3.stat.correlation.KendallsCorrelation</li> |
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| <pre>public class <span class="strong">KendallsCorrelation</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></pre> |
| <div class="block">Implementation of Kendall's Tau-b rank correlation</a>. |
| <p> |
| A pair of observations (x<sub>1</sub>, y<sub>1</sub>) and |
| (x<sub>2</sub>, y<sub>2</sub>) are considered <i>concordant</i> if |
| x<sub>1</sub> < x<sub>2</sub> and y<sub>1</sub> < y<sub>2</sub> |
| or x<sub>2</sub> < x<sub>1</sub> and y<sub>2</sub> < y<sub>1</sub>. |
| The pair is <i>discordant</i> if x<sub>1</sub> < x<sub>2</sub> and |
| y<sub>2</sub> < y<sub>1</sub> or x<sub>2</sub> < x<sub>1</sub> and |
| y<sub>1</sub> < y<sub>2</sub>. If either x<sub>1</sub> = x<sub>2</sub> |
| or y<sub>1</sub> = y<sub>2</sub>, the pair is neither concordant nor |
| discordant. |
| <p> |
| Kendall's Tau-b is defined as: |
| <pre> |
| tau<sub>b</sub> = (n<sub>c</sub> - n<sub>d</sub>) / sqrt((n<sub>0</sub> - n<sub>1</sub>) * (n<sub>0</sub> - n<sub>2</sub>)) |
| </pre> |
| <p> |
| where: |
| <ul> |
| <li>n<sub>0</sub> = n * (n - 1) / 2</li> |
| <li>n<sub>c</sub> = Number of concordant pairs</li> |
| <li>n<sub>d</sub> = Number of discordant pairs</li> |
| <li>n<sub>1</sub> = sum of t<sub>i</sub> * (t<sub>i</sub> - 1) / 2 for all i</li> |
| <li>n<sub>2</sub> = sum of u<sub>j</sub> * (u<sub>j</sub> - 1) / 2 for all j</li> |
| <li>t<sub>i</sub> = Number of tied values in the i<sup>th</sup> group of ties in x</li> |
| <li>u<sub>j</sub> = Number of tied values in the j<sup>th</sup> group of ties in y</li> |
| </ul> |
| <p> |
| This implementation uses the O(n log n) algorithm described in |
| William R. Knight's 1966 paper "A Computer Method for Calculating |
| Kendall's Tau with Ungrouped Data" in the Journal of the American |
| Statistical Association.</div> |
| <dl><dt><span class="strong">Since:</span></dt> |
| <dd>3.3</dd> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: KendallsCorrelation.java 1548907 2013-12-07 13:08:06Z tn $</dd> |
| <dt><span class="strong">See Also:</span></dt><dd><a href="http://en.wikipedia.org/wiki/Kendall_tau_rank_correlation_coefficient"> |
| Kendall tau rank correlation coefficient (Wikipedia)</a>, |
| <a href="http://www.jstor.org/stable/2282833">A Computer |
| Method for Calculating Kendall's Tau with Ungrouped Data</a></dd></dl> |
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| <td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/KendallsCorrelation.html#KendallsCorrelation()">KendallsCorrelation</a></strong>()</code> |
| <div class="block">Create a KendallsCorrelation instance without data.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/KendallsCorrelation.html#KendallsCorrelation(double[][])">KendallsCorrelation</a></strong>(double[][] data)</code> |
| <div class="block">Create a KendallsCorrelation from a rectangular array |
| whose columns represent values of variables to be correlated.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/KendallsCorrelation.html#KendallsCorrelation(org.apache.commons.math3.linear.RealMatrix)">KendallsCorrelation</a></strong>(<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix)</code> |
| <div class="block">Create a KendallsCorrelation from a RealMatrix whose columns |
| represent variables to be correlated.</div> |
| </td> |
| </tr> |
| </table> |
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| <td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/KendallsCorrelation.html#computeCorrelationMatrix(double[][])">computeCorrelationMatrix</a></strong>(double[][] matrix)</code> |
| <div class="block">Computes the Kendall's Tau rank correlation matrix for the columns of |
| the input rectangular array.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/KendallsCorrelation.html#computeCorrelationMatrix(org.apache.commons.math3.linear.RealMatrix)">computeCorrelationMatrix</a></strong>(<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix)</code> |
| <div class="block">Computes the Kendall's Tau rank correlation matrix for the columns of |
| the input matrix.</div> |
| </td> |
| </tr> |
| <tr class="altColor"> |
| <td class="colFirst"><code>double</code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/KendallsCorrelation.html#correlation(double[], double[])">correlation</a></strong>(double[] xArray, |
| double[] yArray)</code> |
| <div class="block">Computes the Kendall's Tau rank correlation coefficient between the two arrays.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td> |
| <td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/stat/correlation/KendallsCorrelation.html#getCorrelationMatrix()">getCorrelationMatrix</a></strong>()</code> |
| <div class="block">Returns the correlation matrix.</div> |
| </td> |
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| <a name="KendallsCorrelation()"> |
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| <h4>KendallsCorrelation</h4> |
| <pre>public KendallsCorrelation()</pre> |
| <div class="block">Create a KendallsCorrelation instance without data.</div> |
| </li> |
| </ul> |
| <a name="KendallsCorrelation(double[][])"> |
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| <h4>KendallsCorrelation</h4> |
| <pre>public KendallsCorrelation(double[][] data)</pre> |
| <div class="block">Create a KendallsCorrelation from a rectangular array |
| whose columns represent values of variables to be correlated.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>data</code> - rectangular array with columns representing variables</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - if the input data array is not |
| rectangular with at least two rows and two columns.</dd></dl> |
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| <h4>KendallsCorrelation</h4> |
| <pre>public KendallsCorrelation(<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix)</pre> |
| <div class="block">Create a KendallsCorrelation from a RealMatrix whose columns |
| represent variables to be correlated.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - matrix with columns representing variables to correlate</dd></dl> |
| </li> |
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| <h4>getCorrelationMatrix</h4> |
| <pre>public <a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> getCorrelationMatrix()</pre> |
| <div class="block">Returns the correlation matrix.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>correlation matrix</dd></dl> |
| </li> |
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| <a name="computeCorrelationMatrix(org.apache.commons.math3.linear.RealMatrix)"> |
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| <h4>computeCorrelationMatrix</h4> |
| <pre>public <a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> computeCorrelationMatrix(<a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix)</pre> |
| <div class="block">Computes the Kendall's Tau rank correlation matrix for the columns of |
| the input matrix.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - matrix with columns representing variables to correlate</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>correlation matrix</dd></dl> |
| </li> |
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| <a name="computeCorrelationMatrix(double[][])"> |
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| <h4>computeCorrelationMatrix</h4> |
| <pre>public <a href="../../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> computeCorrelationMatrix(double[][] matrix)</pre> |
| <div class="block">Computes the Kendall's Tau rank correlation matrix for the columns of |
| the input rectangular array. The columns of the array represent values |
| of variables to be correlated.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - matrix with columns representing variables to correlate</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>correlation matrix</dd></dl> |
| </li> |
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| <h4>correlation</h4> |
| <pre>public double correlation(double[] xArray, |
| double[] yArray) |
| throws <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></pre> |
| <div class="block">Computes the Kendall's Tau rank correlation coefficient between the two arrays.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>xArray</code> - first data array</dd><dd><code>yArray</code> - second data array</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>Returns Kendall's Tau rank correlation coefficient for the two arrays</dd> |
| <dt><span class="strong">Throws:</span></dt> |
| <dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the arrays lengths do not match</dd></dl> |
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