src/main/java/org/apache/commons/math/distribution/TDistributionImpl.java - platform/external/apache-commons-math - Git at Google

 /*
  * Licensed to the Apache Software Foundation (ASF) under one or more
  * contributor license agreements.  See the NOTICE file distributed with
  * this work for additional information regarding copyright ownership.
  * The ASF licenses this file to You under the Apache License, Version 2.0
  * (the "License"); you may not use this file except in compliance with
  * the License.  You may obtain a copy of the License at
  *
  *      http://www.apache.org/licenses/LICENSE-2.0
  *
  * Unless required by applicable law or agreed to in writing, software
  * distributed under the License is distributed on an "AS IS" BASIS,
  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  * See the License for the specific language governing permissions and
  * limitations under the License.
  */
 package org.apache.commons.math.distribution;

 import java.io.Serializable;

 import org.apache.commons.math.MathException;
 import org.apache.commons.math.MathRuntimeException;
 import org.apache.commons.math.exception.util.LocalizedFormats;
 import org.apache.commons.math.special.Beta;
 import org.apache.commons.math.special.Gamma;
 import org.apache.commons.math.util.FastMath;

 /**
  * Default implementation of
  * {@link org.apache.commons.math.distribution.TDistribution}.
  *
  * @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $
  */
 public class TDistributionImpl
     extends AbstractContinuousDistribution
     implements TDistribution, Serializable  {

     /**
      * Default inverse cumulative probability accuracy
      * @since 2.1
     */
     public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;

     /** Serializable version identifier */
     private static final long serialVersionUID = -5852615386664158222L;

     /** The degrees of freedom*/
     private double degreesOfFreedom;

     /** Inverse cumulative probability accuracy */
     private final double solverAbsoluteAccuracy;

     /**
      * Create a t distribution using the given degrees of freedom and the
      * specified inverse cumulative probability absolute accuracy.
      *
      * @param degreesOfFreedom the degrees of freedom.
      * @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates
      * (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY})
      * @since 2.1
      */
     public TDistributionImpl(double degreesOfFreedom, double inverseCumAccuracy) {
         super();
         setDegreesOfFreedomInternal(degreesOfFreedom);
         solverAbsoluteAccuracy = inverseCumAccuracy;
     }

     /**
      * Create a t distribution using the given degrees of freedom.
      * @param degreesOfFreedom the degrees of freedom.
      */
     public TDistributionImpl(double degreesOfFreedom) {
         this(degreesOfFreedom, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
     }

     /**
      * Modify the degrees of freedom.
      * @param degreesOfFreedom the new degrees of freedom.
      * @deprecated as of 2.1 (class will become immutable in 3.0)
      */
     @Deprecated
     public void setDegreesOfFreedom(double degreesOfFreedom) {
         setDegreesOfFreedomInternal(degreesOfFreedom);
     }

     /**
      * Modify the degrees of freedom.
      * @param newDegreesOfFreedom the new degrees of freedom.
      */
     private void setDegreesOfFreedomInternal(double newDegreesOfFreedom) {
         if (newDegreesOfFreedom <= 0.0) {
             throw MathRuntimeException.createIllegalArgumentException(
                   LocalizedFormats.NOT_POSITIVE_DEGREES_OF_FREEDOM,
                   newDegreesOfFreedom);
         }
         this.degreesOfFreedom = newDegreesOfFreedom;
     }

     /**
      * Access the degrees of freedom.
      * @return the degrees of freedom.
      */
     public double getDegreesOfFreedom() {
         return degreesOfFreedom;
     }

     /**
      * Returns the probability density for a particular point.
      *
      * @param x The point at which the density should be computed.
      * @return The pdf at point x.
      * @since 2.1
      */
     @Override
     public double density(double x) {
         final double n = degreesOfFreedom;
         final double nPlus1Over2 = (n + 1) / 2;
         return FastMath.exp(Gamma.logGamma(nPlus1Over2) - 0.5 * (FastMath.log(FastMath.PI) + FastMath.log(n)) -
                 Gamma.logGamma(n/2) - nPlus1Over2 * FastMath.log(1 + x * x /n));
     }

     /**
      * For this distribution, X, this method returns P(X &lt; <code>x</code>).
      * @param x the value at which the CDF is evaluated.
      * @return CDF evaluated at <code>x</code>.
      * @throws MathException if the cumulative probability can not be
      *            computed due to convergence or other numerical errors.
      */
     public double cumulativeProbability(double x) throws MathException{
         double ret;
         if (x == 0.0) {
             ret = 0.5;
         } else {
             double t =
                 Beta.regularizedBeta(
                     degreesOfFreedom / (degreesOfFreedom + (x * x)),
                     0.5 * degreesOfFreedom,
                     0.5);
             if (x < 0.0) {
                 ret = 0.5 * t;
             } else {
                 ret = 1.0 - 0.5 * t;
             }
         }

         return ret;
     }

     /**
      * For this distribution, X, this method returns the critical point x, such
      * that P(X &lt; x) = <code>p</code>.
      * <p>
      * Returns <code>Double.NEGATIVE_INFINITY</code> for p=0 and
      * <code>Double.POSITIVE_INFINITY</code> for p=1.</p>
      *
      * @param p the desired probability
      * @return x, such that P(X &lt; x) = <code>p</code>
      * @throws MathException if the inverse cumulative probability can not be
      *         computed due to convergence or other numerical errors.
      * @throws IllegalArgumentException if <code>p</code> is not a valid
      *         probability.
      */
     @Override
     public double inverseCumulativeProbability(final double p)
     throws MathException {
         if (p == 0) {
             return Double.NEGATIVE_INFINITY;
         }
         if (p == 1) {
             return Double.POSITIVE_INFINITY;
         }
         return super.inverseCumulativeProbability(p);
     }

     /**
      * Access the domain value lower bound, based on <code>p</code>, used to
      * bracket a CDF root.  This method is used by
      * {@link #inverseCumulativeProbability(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>
      */
     @Override
     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 #inverseCumulativeProbability(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>
      */
     @Override
     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 #inverseCumulativeProbability(double)} to find critical values.
      *
      * @param p the desired probability for the critical value
      * @return initial domain value
      */
     @Override
     protected double getInitialDomain(double p) {
         return 0.0;
     }

     /**
      * Return the absolute accuracy setting of the solver used to estimate
      * inverse cumulative probabilities.
      *
      * @return the solver absolute accuracy
      * @since 2.1
      */
     @Override
     protected double getSolverAbsoluteAccuracy() {
         return solverAbsoluteAccuracy;
     }

     /**
      * Returns the lower bound of the support for the distribution.
      *
      * The lower bound of the support is always negative infinity
      * no matter the parameters.
      *
      * @return lower bound of the support (always Double.NEGATIVE_INFINITY)
      * @since 2.2
      */
     public double getSupportLowerBound() {
         return Double.NEGATIVE_INFINITY;
     }

     /**
      * Returns the upper bound of the support for the distribution.
      *
      * The upper bound of the support is always positive infinity
      * no matter the parameters.
      *
      * @return upper bound of the support (always Double.POSITIVE_INFINITY)
      * @since 2.2
      */
     public double getSupportUpperBound() {
         return Double.POSITIVE_INFINITY;
     }

     /**
      * Returns the mean.
      *
      * For degrees of freedom parameter df, the mean is
      * <ul>
      *  <li>if <code>df &gt; 1</code> then <code>0</code></li>
      * <li>else <code>undefined</code></li>
      * </ul>
      *
      * @return the mean
      * @since 2.2
      */
     public double getNumericalMean() {
         final double df = getDegreesOfFreedom();

         if (df > 1) {
             return 0;
         }

         return Double.NaN;
     }

     /**
      * Returns the variance.
      *
      * For degrees of freedom parameter df, the variance is
      * <ul>
      *  <li>if <code>df &gt; 2</code> then <code>df / (df - 2)</code> </li>
      *  <li>if <code>1 &lt; df &lt;= 2</code> then <code>positive infinity</code></li>
      *  <li>else <code>undefined</code></li>
      * </ul>
      *
      * @return the variance
      * @since 2.2
      */
     public double getNumericalVariance() {
         final double df = getDegreesOfFreedom();

         if (df > 2) {
             return df / (df - 2);
         }

         if (df > 1 && df <= 2) {
             return Double.POSITIVE_INFINITY;
         }

         return Double.NaN;
     }

 }
	/*
	* Licensed to the Apache Software Foundation (ASF) under one or more
	* contributor license agreements. See the NOTICE file distributed with
	* this work for additional information regarding copyright ownership.
	* The ASF licenses this file to You under the Apache License, Version 2.0
	* (the "License"); you may not use this file except in compliance with
	* the License. You may obtain a copy of the License at
	*
	* http://www.apache.org/licenses/LICENSE-2.0
	*
	* Unless required by applicable law or agreed to in writing, software
	* distributed under the License is distributed on an "AS IS" BASIS,
	* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
	* See the License for the specific language governing permissions and
	* limitations under the License.
	*/
	package org.apache.commons.math.distribution;

	import java.io.Serializable;

	import org.apache.commons.math.MathException;
	import org.apache.commons.math.MathRuntimeException;
	import org.apache.commons.math.exception.util.LocalizedFormats;
	import org.apache.commons.math.special.Beta;
	import org.apache.commons.math.special.Gamma;
	import org.apache.commons.math.util.FastMath;

	/**
	* Default implementation of
	* {@link org.apache.commons.math.distribution.TDistribution}.
	*
	* @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $
	*/
	public class TDistributionImpl
	extends AbstractContinuousDistribution
	implements TDistribution, Serializable {

	/**
	* Default inverse cumulative probability accuracy
	* @since 2.1
	*/
	public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;

	/** Serializable version identifier */
	private static final long serialVersionUID = -5852615386664158222L;

	/** The degrees of freedom*/
	private double degreesOfFreedom;

	/** Inverse cumulative probability accuracy */
	private final double solverAbsoluteAccuracy;

	/**
	* Create a t distribution using the given degrees of freedom and the
	* specified inverse cumulative probability absolute accuracy.
	*
	* @param degreesOfFreedom the degrees of freedom.
	* @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates
	* (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY})
	* @since 2.1
	*/
	public TDistributionImpl(double degreesOfFreedom, double inverseCumAccuracy) {
	super();
	setDegreesOfFreedomInternal(degreesOfFreedom);
	solverAbsoluteAccuracy = inverseCumAccuracy;
	}

	/**
	* Create a t distribution using the given degrees of freedom.
	* @param degreesOfFreedom the degrees of freedom.
	*/
	public TDistributionImpl(double degreesOfFreedom) {
	this(degreesOfFreedom, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
	}

	/**
	* Modify the degrees of freedom.
	* @param degreesOfFreedom the new degrees of freedom.
	* @deprecated as of 2.1 (class will become immutable in 3.0)
	*/
	@Deprecated
	public void setDegreesOfFreedom(double degreesOfFreedom) {
	setDegreesOfFreedomInternal(degreesOfFreedom);
	}

	/**
	* Modify the degrees of freedom.
	* @param newDegreesOfFreedom the new degrees of freedom.
	*/
	private void setDegreesOfFreedomInternal(double newDegreesOfFreedom) {
	if (newDegreesOfFreedom <= 0.0) {
	throw MathRuntimeException.createIllegalArgumentException(
	LocalizedFormats.NOT_POSITIVE_DEGREES_OF_FREEDOM,
	newDegreesOfFreedom);
	}
	this.degreesOfFreedom = newDegreesOfFreedom;
	}

	/**
	* Access the degrees of freedom.
	* @return the degrees of freedom.
	*/
	public double getDegreesOfFreedom() {
	return degreesOfFreedom;
	}

	/**
	* Returns the probability density for a particular point.
	*
	* @param x The point at which the density should be computed.
	* @return The pdf at point x.
	* @since 2.1
	*/
	@Override
	public double density(double x) {
	final double n = degreesOfFreedom;
	final double nPlus1Over2 = (n + 1) / 2;
	return FastMath.exp(Gamma.logGamma(nPlus1Over2) - 0.5 * (FastMath.log(FastMath.PI) + FastMath.log(n)) -
	Gamma.logGamma(n/2) - nPlus1Over2 * FastMath.log(1 + x * x /n));
	}

	/**
	* For this distribution, X, this method returns P(X < <code>x</code>).
	* @param x the value at which the CDF is evaluated.
	* @return CDF evaluated at <code>x</code>.
	* @throws MathException if the cumulative probability can not be
	* computed due to convergence or other numerical errors.
	*/
	public double cumulativeProbability(double x) throws MathException{
	double ret;
	if (x == 0.0) {
	ret = 0.5;
	} else {
	double t =
	Beta.regularizedBeta(
	degreesOfFreedom / (degreesOfFreedom + (x * x)),
	0.5 * degreesOfFreedom,
	0.5);
	if (x < 0.0) {
	ret = 0.5 * t;
	} else {
	ret = 1.0 - 0.5 * t;
	}
	}

	return ret;
	}

	/**
	* For this distribution, X, this method returns the critical point x, such
	* that P(X < x) = <code>p</code>.
	* <p>
	* Returns <code>Double.NEGATIVE_INFINITY</code> for p=0 and
	* <code>Double.POSITIVE_INFINITY</code> for p=1.</p>
	*
	* @param p the desired probability
	* @return x, such that P(X < x) = <code>p</code>
	* @throws MathException if the inverse cumulative probability can not be
	* computed due to convergence or other numerical errors.
	* @throws IllegalArgumentException if <code>p</code> is not a valid
	* probability.
	*/
	@Override
	public double inverseCumulativeProbability(final double p)
	throws MathException {
	if (p == 0) {
	return Double.NEGATIVE_INFINITY;
	}
	if (p == 1) {
	return Double.POSITIVE_INFINITY;
	}
	return super.inverseCumulativeProbability(p);
	}

	/**
	* Access the domain value lower bound, based on <code>p</code>, used to
	* bracket a CDF root. This method is used by
	* {@link #inverseCumulativeProbability(double)} to find critical values.
	*
	* @param p the desired probability for the critical value
	* @return domain value lower bound, i.e.
	* P(X < <i>lower bound</i>) < <code>p</code>
	*/
	@Override
	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 #inverseCumulativeProbability(double)} to find critical values.
	*
	* @param p the desired probability for the critical value
	* @return domain value upper bound, i.e.
	* P(X < <i>upper bound</i>) > <code>p</code>
	*/
	@Override
	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 #inverseCumulativeProbability(double)} to find critical values.
	*
	* @param p the desired probability for the critical value
	* @return initial domain value
	*/
	@Override
	protected double getInitialDomain(double p) {
	return 0.0;
	}

	/**
	* Return the absolute accuracy setting of the solver used to estimate
	* inverse cumulative probabilities.
	*
	* @return the solver absolute accuracy
	* @since 2.1
	*/
	@Override
	protected double getSolverAbsoluteAccuracy() {
	return solverAbsoluteAccuracy;
	}

	/**
	* Returns the lower bound of the support for the distribution.
	*
	* The lower bound of the support is always negative infinity
	* no matter the parameters.
	*
	* @return lower bound of the support (always Double.NEGATIVE_INFINITY)
	* @since 2.2
	*/
	public double getSupportLowerBound() {
	return Double.NEGATIVE_INFINITY;
	}

	/**
	* Returns the upper bound of the support for the distribution.
	*
	* The upper bound of the support is always positive infinity
	* no matter the parameters.
	*
	* @return upper bound of the support (always Double.POSITIVE_INFINITY)
	* @since 2.2
	*/
	public double getSupportUpperBound() {
	return Double.POSITIVE_INFINITY;
	}

	/**
	* Returns the mean.
	*
	* For degrees of freedom parameter df, the mean is
	* <ul>
	* <li>if <code>df > 1</code> then <code>0</code></li>
	* <li>else <code>undefined</code></li>
	* </ul>
	*
	* @return the mean
	* @since 2.2
	*/
	public double getNumericalMean() {
	final double df = getDegreesOfFreedom();

	if (df > 1) {
	return 0;
	}

	return Double.NaN;
	}

	/**
	* Returns the variance.
	*
	* For degrees of freedom parameter df, the variance is
	* <ul>
	* <li>if <code>df > 2</code> then <code>df / (df - 2)</code> </li>
	* <li>if <code>1 < df <= 2</code> then <code>positive infinity</code></li>
	* <li>else <code>undefined</code></li>
	* </ul>
	*
	* @return the variance
	* @since 2.2
	*/
	public double getNumericalVariance() {
	final double df = getDegreesOfFreedom();

	if (df > 2) {
	return df / (df - 2);
	}

	if (df > 1 && df <= 2) {
	return Double.POSITIVE_INFINITY;
	}

	return Double.NaN;
	}

	}