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From mdigg...@apache.org
Subject cvs commit: jakarta-commons-sandbox/math/src/java/org/apache/commons/math/stat/distribution TDistributionImpl.java TDistribution.java DistributionFactory.java DistributionFactoryImpl.java
Date Sat, 07 Jun 2003 13:57:54 GMT
mdiggory    2003/06/07 06:57:54

  Modified:    math/src/test/org/apache/commons/math/stat/distribution
                        DistributionFactoryImplTest.java
               math/src/java/org/apache/commons/math/stat/distribution
                        DistributionFactory.java
                        DistributionFactoryImpl.java
  Added:       math/src/java/org/apache/commons/math/special Beta.java
               math/src/test/org/apache/commons/math/stat/distribution
                        TDistributionTest.java
               math/src/java/org/apache/commons/math/stat/distribution
                        TDistributionImpl.java TDistribution.java
  Log:
  PR: http://nagoya.apache.org/bugzilla/show_bug.cgi?id=20570
  Submitted by:	brent@worden.org
  
  Revision  Changes    Path
  1.1                  jakarta-commons-sandbox/math/src/java/org/apache/commons/math/special/Beta.java
  
  Index: Beta.java
  ===================================================================
  /* ====================================================================
   * The Apache Software License, Version 1.1
   *
   * Copyright (c) 2003 The Apache Software Foundation.  All rights
   * reserved.
   *
   * Redistribution and use in source and binary forms, with or without
   * modification, are permitted provided that the following conditions
   * are met:
   *
   * 1. Redistributions of source code must retain the above copyright
   *    notice, this list of conditions and the following disclaimer.
   *
   * 2. Redistributions in binary form must reproduce the above copyright
   *    notice, this list of conditions and the following disclaimer in
   *    the documentation and/or other materials provided with the
   *    distribution.
   *
   * 3. The end-user documentation included with the redistribution, if
   *    any, must include the following acknowlegement:
   *       "This product includes software developed by the
   *        Apache Software Foundation (http://www.apache.org/)."
   *    Alternately, this acknowlegement may appear in the software itself,
   *    if and wherever such third-party acknowlegements normally appear.
   *
   * 4. The names "The Jakarta Project", "Commons", and "Apache Software
   *    Foundation" must not be used to endorse or promote products derived
   *    from this software without prior written permission. For written
   *    permission, please contact apache@apache.org.
   *
   * 5. Products derived from this software may not be called "Apache"
   *    nor may "Apache" appear in their names without prior written
   *    permission of the Apache Software Foundation.
   *
   * THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED
   * WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
   * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
   * DISCLAIMED.  IN NO EVENT SHALL THE APACHE SOFTWARE FOUNDATION OR
   * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
   * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
   * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
   * USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
   * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
   * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
   * OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
   * SUCH DAMAGE.
   * ====================================================================
   *
   * This software consists of voluntary contributions made by many
   * individuals on behalf of the Apache Software Foundation.  For more
   * information on the Apache Software Foundation, please see
   * <http://www.apache.org/>.
   */
  package org.apache.commons.math.special;
  
  /**
   * This is a utility class that provides computation methods related to the
   * Gamma family of functions.
   * 
   * @author Brent Worden
   */
  public class Beta {
      /** Maximum allowed numerical error. */
      private static final double DEFAULT_EPSILON = 10e-9;
  
      /**
       * Default constructor.  Prohibit instantiation.
       */
      private Beta() {
          super();
      }
  
      /**
       * <p>
       * Returns the regularized beta function I(x, a, b).
       * </p>
       * 
       * @param x ???
       * @param a ???
       * @param b ???
       * @return the regularized beta function I(x, a, b)
       */
      public static double regularizedBeta(double x, double a, double b) {
          return regularizedBeta(x, a, b, DEFAULT_EPSILON, Integer.MAX_VALUE);
      }
  
      /**
       * <p>
       * Returns the regularized beta function I(x, a, b).
       * </p>
       * 
       * @param x ???
       * @param a ???
       * @param b ???
       * @return the regularized beta function I(x, a, b)
       */
      public static double regularizedBeta(double x, double a, double b, double epsilon) {
          return regularizedBeta(x, a, b, epsilon, Integer.MAX_VALUE);
      }
  
      /**
       * <p>
       * Returns the regularized beta function I(x, a, b).
       * </p>
       * 
       * @param x ???
       * @param a ???
       * @param b ???
       * @return the regularized beta function I(x, a, b)
       */
      public static double regularizedBeta(double x, double a, double b, int maxIterations)
{
          return regularizedBeta(x, a, b, DEFAULT_EPSILON, maxIterations);
      }
      
      /**
       * <p>
       * Returns the regularized beta function I(x, a, b).
       * </p>
       * 
       * <p>
       * The implementation of this method is based on:
       * <ul>
       * <li>
       * <a href="http://mathworld.wolfram.com/RegularizedBetaFunction.html">
       * Regularized Beta Function</a>.</li>
       * <li>
       * <a href="http://mathworld.wolfram.com/IncompleteBetaFunction.html">
       * Incomplete Beta Function</a>.</li>
       * </ul>
       * </p>
       * 
       * @param x ???
       * @param a ???
       * @param b ???
       * @return the regularized beta function I(x, a, b)
       */
      public static double regularizedBeta(double x, final double a, final double b, double
epsilon, int maxIterations) {
          double ret;
  
          if (a <= 0.0) {
              throw new IllegalArgumentException("a must be positive");
          } else if (b <= 0.0) {
              throw new IllegalArgumentException("b must be positive");
          } else if (x < 0.0 || x > 1.0) {
              throw new IllegalArgumentException(
                  "x must be between 0.0 and 1.0, inclusive");
          } else if(x == 0.0){
              ret = 0.0;
          } else if(x == 1.0){
              ret = 1.0;
          } else {
              double n = 0.0;
              double an = 1.0 / a;
              double s = an;
              while(Math.abs(an) > epsilon && n < maxIterations){
                  n = n + 1.0;
                  an = an * (n - b) / n * x / (a + n) * (a + n - 1);
                  s = s + an;
              }
              ret = Math.exp(a * Math.log(x) - logBeta(a, b)) * s;
          }
  
          return ret;
      }
  
      /**
       * <p>
       * Returns the natural logarithm of the beta function B(a, b).
       * </p>
       *
       * <p> 
       * The implementation of this method is based on:
       * <ul>
       * <li><a href="http://mathworld.wolfram.com/BetaFunction.html">
       * Beta Function</a>, equation (1).</li>
       * </ul>
       * </p>
       * 
       * @param x ???
       * @return log(B(a, b))
       */
      public static double logBeta(double a, double b) {
          double ret;
  
          if (a <= 0.0) {
              throw new IllegalArgumentException("a must be positive");
          } else if (b <= 0.0) {
              throw new IllegalArgumentException("b must be positive");
          } else {
              ret = Gamma.logGamma(a) + Gamma.logGamma(b)
                  - Gamma.logGamma(a + b);
          }
  
          return ret;
      }
  }
  
  
  
  1.4       +26 -26    jakarta-commons-sandbox/math/src/test/org/apache/commons/math/stat/distribution/DistributionFactoryImplTest.java
  
  Index: DistributionFactoryImplTest.java
  ===================================================================
  RCS file: /home/cvs/jakarta-commons-sandbox/math/src/test/org/apache/commons/math/stat/distribution/DistributionFactoryImplTest.java,v
  retrieving revision 1.3
  retrieving revision 1.4
  diff -u -r1.3 -r1.4
  --- DistributionFactoryImplTest.java	5 Jun 2003 14:03:52 -0000	1.3
  +++ DistributionFactoryImplTest.java	7 Jun 2003 13:57:54 -0000	1.4
  @@ -101,30 +101,30 @@
               fail("positive alpah and beta.  IllegalArgumentException is not expected");
           }
       }
  -//    
  -//    public void testCreateTDistributionNegative(){
  -//        try {
  -//            factory.createTDistribution(-1.0);
  -//            fail("negative degrees of freedom.  IllegalArgumentException expected");
  -//        } catch (IllegalArgumentException ex) {
  -//            ;
  -//        }
  -//    }
  -//    
  -//    public void testCreateTDistributionZero(){
  -//        try {
  -//            factory.createTDistribution(0.0);
  -//            fail("zero degrees of freedom.  IllegalArgumentException expected");
  -//        } catch (IllegalArgumentException ex) {
  -//            ;
  -//        }
  -//    }
  -//    
  -//    public void testCreateTDistributionPositive(){
  -//        try {
  -//            factory.createTDistribution(1.0);
  -//        } catch (IllegalArgumentException ex) {
  -//            fail("positive degrees of freedom.  IllegalArgumentException is not expected");
  -//        }
  -//    }
  +    
  +    public void testCreateTDistributionNegative(){
  +        try {
  +            factory.createTDistribution(-1.0);
  +            fail("negative degrees of freedom.  IllegalArgumentException expected");
  +        } catch (IllegalArgumentException ex) {
  +            ;
  +        }
  +    }
  +    
  +    public void testCreateTDistributionZero(){
  +        try {
  +            factory.createTDistribution(0.0);
  +            fail("zero degrees of freedom.  IllegalArgumentException expected");
  +        } catch (IllegalArgumentException ex) {
  +            ;
  +        }
  +    }
  +    
  +    public void testCreateTDistributionPositive(){
  +        try {
  +            factory.createTDistribution(1.0);
  +        } catch (IllegalArgumentException ex) {
  +            fail("positive degrees of freedom.  IllegalArgumentException is not expected");
  +        }
  +    }
   }
  
  
  
  1.1                  jakarta-commons-sandbox/math/src/test/org/apache/commons/math/stat/distribution/TDistributionTest.java
  
  Index: TDistributionTest.java
  ===================================================================
  /* ====================================================================
   * The Apache Software License, Version 1.1
   *
   * Copyright (c) 2003 The Apache Software Foundation.  All rights
   * reserved.
   *
   * Redistribution and use in source and binary forms, with or without
   * modification, are permitted provided that the following conditions
   * are met:
   *
   * 1. Redistributions of source code must retain the above copyright
   *    notice, this list of conditions and the following disclaimer.
   *
   * 2. Redistributions in binary form must reproduce the above copyright
   *    notice, this list of conditions and the following disclaimer in
   *    the documentation and/or other materials provided with the
   *    distribution.
   *
   * 3. The end-user documentation included with the redistribution, if
   *    any, must include the following acknowlegement:
   *       "This product includes software developed by the
   *        Apache Software Foundation (http://www.apache.org/)."
   *    Alternately, this acknowlegement may appear in the software itself,
   *    if and wherever such third-party acknowlegements normally appear.
   *
   * 4. The names "The Jakarta Project", "Commons", and "Apache Software
   *    Foundation" must not be used to endorse or promote products derived
   *    from this software without prior written permission. For written
   *    permission, please contact apache@apache.org.
   *
   * 5. Products derived from this software may not be called "Apache"
   *    nor may "Apache" appear in their names without prior written
   *    permission of the Apache Software Foundation.
   *
   * THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED
   * WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
   * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
   * DISCLAIMED.  IN NO EVENT SHALL THE APACHE SOFTWARE FOUNDATION OR
   * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
   * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
   * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
   * USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
   * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
   * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
   * OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
   * SUCH DAMAGE.
   * ====================================================================
   *
   * This software consists of voluntary contributions made by many
   * individuals on behalf of the Apache Software Foundation.  For more
   * information on the Apache Software Foundation, please see
   * <http://www.apache.org/>.
   */
  package org.apache.commons.math.stat.distribution;
  
  import junit.framework.TestCase;
  
  /**
   * @author Brent Worden
   */
  public class TDistributionTest extends TestCase {
      private TDistribution t;
      
      /**
       * Constructor for ChiSquareDistributionTest.
       * @param name
       */
      public TDistributionTest(String name) {
          super(name);
      }
  
      /*
       * @see TestCase#setUp()
       */
      protected void setUp() throws Exception {
          super.setUp();
          t = DistributionFactory.newInstance().createTDistribution(5.0);
      }
  
      /*
       * @see TestCase#tearDown()
       */
      protected void tearDown() throws Exception {
          t = null;
          super.tearDown();
      }
  
      public void testLowerTailProbability(){
          testProbability(-5.893, .001);
          testProbability(-3.365, .010);
          testProbability(-2.571, .025);
          testProbability(-2.015, .050);
          testProbability(-1.476, .100);
      }
  
      public void testUpperTailProbability(){
          testProbability(5.893, .999);
          testProbability(3.365, .990);
          testProbability(2.571, .975);
          testProbability(2.015, .950);
          testProbability(1.476, .900);
      }
      
      public void testLowerTailValues(){
          testValue(-5.893, .001);
          testValue(-3.365, .010);
          testValue(-2.571, .025);
          testValue(-2.015, .050);
          testValue(-1.476, .100);
      }
      
      public void testUpperTailValues(){
          testValue(5.893, .999);
          testValue(3.365, .990);
          testValue(2.571, .975);
          testValue(2.015, .950);
          testValue(1.476, .900);
      }
      
      private void testProbability(double x, double expected){
          double actual = t.cummulativeProbability(x);
          assertEquals("probability for " + x, expected, actual, 10e-4);
      }
      
      private void testValue(double expected, double p){
          double actual = t.inverseCummulativeProbability(p);
          assertEquals("value for " + p, expected, actual, 10e-4);
      }
  }
  
  
  
  1.4       +7 -0      jakarta-commons-sandbox/math/src/java/org/apache/commons/math/stat/distribution/DistributionFactory.java
  
  Index: DistributionFactory.java
  ===================================================================
  RCS file: /home/cvs/jakarta-commons-sandbox/math/src/java/org/apache/commons/math/stat/distribution/DistributionFactory.java,v
  retrieving revision 1.3
  retrieving revision 1.4
  diff -u -r1.3 -r1.4
  --- DistributionFactory.java	5 Jun 2003 14:02:28 -0000	1.3
  +++ DistributionFactory.java	7 Jun 2003 13:57:54 -0000	1.4
  @@ -110,4 +110,11 @@
        */
       public abstract GammaDistribution createGammaDistribution(
           double alpha, double beta);
  +
  +    /**
  +     * Create a new t distribution with the given degrees of freedom.
  +     * @param degreesOfFreedom degrees of freedom.
  +     * @return a new t distribution.  
  +     */
  +    public abstract TDistribution createTDistribution(double degreesOfFreedom);
   }
  
  
  
  1.4       +9 -0      jakarta-commons-sandbox/math/src/java/org/apache/commons/math/stat/distribution/DistributionFactoryImpl.java
  
  Index: DistributionFactoryImpl.java
  ===================================================================
  RCS file: /home/cvs/jakarta-commons-sandbox/math/src/java/org/apache/commons/math/stat/distribution/DistributionFactoryImpl.java,v
  retrieving revision 1.3
  retrieving revision 1.4
  diff -u -r1.3 -r1.4
  --- DistributionFactoryImpl.java	5 Jun 2003 14:02:29 -0000	1.3
  +++ DistributionFactoryImpl.java	7 Jun 2003 13:57:54 -0000	1.4
  @@ -90,4 +90,13 @@
   
           return new GammaDistributionImpl(alpha, beta);
       }
  +
  +    /**
  +     * Create a new t distribution with the given degrees of freedom.
  +     * @param degreesOfFreedom degrees of freedom.
  +     * @return a new t distribution.  
  +     */
  +    public TDistribution createTDistribution(double degreesOfFreedom) {
  +        return new TDistributionImpl(degreesOfFreedom);
  +    }
   }
  
  
  
  1.1                  jakarta-commons-sandbox/math/src/java/org/apache/commons/math/stat/distribution/TDistributionImpl.java
  
  Index: TDistributionImpl.java
  ===================================================================
  /* ====================================================================
   * The Apache Software License, Version 1.1
   *
   * Copyright (c) 2003 The Apache Software Foundation.  All rights
   * reserved.
   *
   * Redistribution and use in source and binary forms, with or without
   * modification, are permitted provided that the following conditions
   * are met:
   *
   * 1. Redistributions of source code must retain the above copyright
   *    notice, this list of conditions and the following disclaimer.
   *
   * 2. Redistributions in binary form must reproduce the above copyright
   *    notice, this list of conditions and the following disclaimer in
   *    the documentation and/or other materials provided with the
   *    distribution.
   *
   * 3. The end-user documentation included with the redistribution, if
   *    any, must include the following acknowlegement:
   *       "This product includes software developed by the
   *        Apache Software Foundation (http://www.apache.org/)."
   *    Alternately, this acknowlegement may appear in the software itself,
   *    if and wherever such third-party acknowlegements normally appear.
   *
   * 4. The names "The Jakarta Project", "Commons", and "Apache Software
   *    Foundation" must not be used to endorse or promote products derived
   *    from this software without prior written permission. For written
   *    permission, please contact apache@apache.org.
   *
   * 5. Products derived from this software may not be called "Apache"
   *    nor may "Apache" appear in their names without prior written
   *    permission of the Apache Software Foundation.
   *
   * THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED
   * WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
   * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
   * DISCLAIMED.  IN NO EVENT SHALL THE APACHE SOFTWARE FOUNDATION OR
   * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
   * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
   * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
   * USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
   * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
   * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
   * OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
   * SUCH DAMAGE.
   * ====================================================================
   *
   * This software consists of voluntary contributions made by many
   * individuals on behalf of the Apache Software Foundation.  For more
   * information on the Apache Software Foundation, please see
   * <http://www.apache.org/>.
   */
  package org.apache.commons.math.stat.distribution;
  
  import org.apache.commons.math.special.Beta;
  
  /**
   * Default implementation of
   * {@link org.apache.commons.math.stat.distribution.TDistribution}.
   * 
   * @author Brent Worden
   */
  public class TDistributionImpl
      extends AbstractContinuousDistribution
      implements TDistribution {
  
      /** The degrees of freedom*/
      private double degreesOfFreedom;
      
      /**
       * Create a t distribution using the given degrees of freedom.
       * @param degreesOfFreedom the degrees of freedom.
       */
      public TDistributionImpl(double degreesOfFreedom){
          super();
          setDegreesOfFreedom(degreesOfFreedom);
      }
  
      /**
       * Modify the degrees of freedom.
       * @param degreesOfFreedom the new degrees of freedom.
       */
      public void setDegreesOfFreedom(double degreesOfFreedom) {
          if(degreesOfFreedom <= 0.0){
              throw new IllegalArgumentException(
                  "degrees of freedom must be positive.");
          }
          this.degreesOfFreedom = degreesOfFreedom;
      }
  
      /**
       * Access the degrees of freedom.
       * @return the degrees of freedom.
       */
      public double getDegreesOfFreedom() {
          return degreesOfFreedom;
      }
  
      /**
       * For this disbution, X, this method returns P(X &lt; <code>x</code>).
       * @param x the value at which the CDF is evaluated.
       * @return CDF evaluted at <code>x</code>. 
       */
      public double cummulativeProbability(double x) {
          double t = Beta.regularizedBeta(
              getDegreesOfFreedom() / (getDegreesOfFreedom() + (x * x)),
              0.5 * getDegreesOfFreedom(), 0.5);
              
          double ret;
          if(x < 0.0){
              ret = 0.5 * t;
          } else if(x > 0.0){
              ret = 1.0 - 0.5 * t;
          } else {
              ret = 0.5;
          }
          return ret;
      }
          
      /**
       * Access the domain value lower bound, based on <code>p</code>, used to
       * bracket a CDF root.  This method is used by
       * {@link #inverseCummulativeProbability(double)} to find critical values.
       * 
       * @param p the desired probability for the critical value
       * @return domain value lower bound, i.e.
       *         P(X &lt; <i>lower bound</i>) &lt; <code>p</code>

       */
      protected double getDomainLowerBound(double p){
          return -Double.MAX_VALUE;
      }
  
      /**
       * Access the domain value upper bound, based on <code>p</code>, used to
       * bracket a CDF root.  This method is used by
       * {@link #inverseCummulativeProbability(double)} to find critical values.
       * 
       * @param p the desired probability for the critical value
       * @return domain value upper bound, i.e.
       *         P(X &lt; <i>upper bound</i>) &gt; <code>p</code>

       */
      protected double getDomainUpperBound(double p){
          return Double.MAX_VALUE;
      }
  
      /**
       * Access the initial domain value, based on <code>p</code>, used to
       * bracket a CDF root.  This method is used by
       * {@link #inverseCummulativeProbability(double)} to find critical values.
       * 
       * @param p the desired probability for the critical value
       * @return initial domain value
       */
      protected double getInitialDomain(double p){
          return 0.0;
      }
  }
  
  
  
  1.1                  jakarta-commons-sandbox/math/src/java/org/apache/commons/math/stat/distribution/TDistribution.java
  
  Index: TDistribution.java
  ===================================================================
  /* ====================================================================
   * The Apache Software License, Version 1.1
   *
   * Copyright (c) 2003 The Apache Software Foundation.  All rights
   * reserved.
   *
   * Redistribution and use in source and binary forms, with or without
   * modification, are permitted provided that the following conditions
   * are met:
   *
   * 1. Redistributions of source code must retain the above copyright
   *    notice, this list of conditions and the following disclaimer.
   *
   * 2. Redistributions in binary form must reproduce the above copyright
   *    notice, this list of conditions and the following disclaimer in
   *    the documentation and/or other materials provided with the
   *    distribution.
   *
   * 3. The end-user documentation included with the redistribution, if
   *    any, must include the following acknowlegement:
   *       "This product includes software developed by the
   *        Apache Software Foundation (http://www.apache.org/)."
   *    Alternately, this acknowlegement may appear in the software itself,
   *    if and wherever such third-party acknowlegements normally appear.
   *
   * 4. The names "The Jakarta Project", "Commons", and "Apache Software
   *    Foundation" must not be used to endorse or promote products derived
   *    from this software without prior written permission. For written
   *    permission, please contact apache@apache.org.
   *
   * 5. Products derived from this software may not be called "Apache"
   *    nor may "Apache" appear in their names without prior written
   *    permission of the Apache Software Foundation.
   *
   * THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED
   * WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
   * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
   * DISCLAIMED.  IN NO EVENT SHALL THE APACHE SOFTWARE FOUNDATION OR
   * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
   * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
   * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
   * USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
   * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
   * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
   * OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
   * SUCH DAMAGE.
   * ====================================================================
   *
   * This software consists of voluntary contributions made by many
   * individuals on behalf of the Apache Software Foundation.  For more
   * information on the Apache Software Foundation, please see
   * <http://www.apache.org/>.
   */
  package org.apache.commons.math.stat.distribution;
  
  /**
   * <p>
   * Student's t-Distribution.
   * </p>
   * 
   * <p>
   * Instances of TDistribution objects should be created using
   * {@link DistributionFactory#createTDistribution(double)}
   * </p>
   * 
   * <p>
   * Reference:<br/>
   * <a href="http://mathworld.wolfram.com/Studentst-Distribution.html">
   * Student's t-Distribution</a>
   * </p>
   * 
   * @author Brent Worden
   */
  public interface TDistribution extends ContinuousDistribution {
      /**
       * Modify the degrees of freedom.
       * @param degreesOfFreedom the new degrees of freedom.
       */
      void setDegreesOfFreedom(double degreesOfFreedom);
      
      /**
       * Access the degrees of freedom.
       * @return the degrees of freedom.
       */
      double getDegreesOfFreedom();
  }
  
  
  

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