studentt.java

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/**    
  * Copyright (C) 2006, Laboratorio di Valutazione delle Prestazioni - Politecnico di Milano

  * This program is free software; you can redistribute it and/or modify
  * it under the terms of the GNU General Public License as published by
  * the Free Software Foundation; either version 2 of the License, or
  * (at your option) any later version.

  * This program is distributed in the hope that it will be useful,
  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  * GNU General Public License for more details.

  * You should have received a copy of the GNU General Public License
  * along with this program; if not, write to the Free Software
  * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
  */
  
package jmt.engine.random;

import jmt.common.exception.IncorrectDistributionParameterException;
import jmt.engine.math.Probability;
import jmt.engine.math.Sfun;
import jmt.engine.random.engine.RandomEngine;


/**
 *
 * This is the StudentT distribution (for his pdf definition please
 * see the constructor description).
 *
 * <br><br>Copyright (c) 2003
 * <br>Politecnico di Milano - dipartimento di Elettronica e Informazione
 * @author Fabrizio Frontera - [e-mail]
 * @author Modified by Stefano Omini, 7/5/2004
 * @author Modified by Bertoli Marco, 8/9/2005
 */

public class StudentT extends Distribution {


	/**
	 * This is the constructor. It creates a new student T distribution which
	 * is defined from is pdf:
	 * <pre>             G((f+1)/2)                    1
	 * pdf(x)= -------------------- *  -------------------------
	 *          (sqrt(pi*f)*G(f/2)      (1+((x^2)/f))^((f+1)/2)</pre>
	 * where G(a) is the gamma (also called "Eulero") function.
	 * f is called degrees of "freedom".
	 */

	public StudentT() {
		engine = RandomEngine.makeDefault();
	}


	/**
	 * it returns the pdf of the distribution.
	 * This method is used to obtain from the distribution his probability distribution
	 * function evaluated where required by the user.
	 *
	 * @param x double indicating where to evaluate the pdf.
	 * @param p parameter of the student T distribution.
	 * @throws IncorrectDistributionParameterException
	 * @return double with the probability distribution function evaluated in x.
	 */

	//OLD
    //public double pdf(double x, StudentTPar p)
    public double pdf(double x, Parameter p)
	        throws IncorrectDistributionParameterException {
		if (p.check()) {
			//OLD
            //double freedom = p.getFreedom();
            double freedom = ((StudentTPar) p).getFreedom();
			double val = Sfun.logGamma((freedom + 1) / 2) - Sfun.logGamma(freedom / 2);
			double TERM = Math.exp(val) / Math.sqrt(Math.PI * freedom);
			return TERM * Math.pow((1 + x * x / freedom), -(freedom + 1) * 0.5);
		} else {
			throw new IncorrectDistributionParameterException("Remember: the number of degrees of freedom must be an integer gtz");
		}
	}

	/**
	 * it returns the cdf of the distribution.
	 * This method is used to obtain from the distribution his cumulative distribution
	 * function evaluated where required by the user.
	 *
	 * @param x double indicating where to evaluate the cdf.
	 * @param p parameter of the student T distribution.
	 * @throws IncorrectDistributionParameterException
	 * @return double with the cumulative distribution function evaluated in x.
	 */

	//OLD
    //public double cdf(double x, StudentTPar p)
    public double cdf(double x, Parameter p)
	        throws IncorrectDistributionParameterException {
		if (p.check()) {
			//OLD
            //double freedom = p.getFreedom();
            double freedom = ((StudentTPar) p).getFreedom();
			return Probability.studentT(freedom, x);
		} else {
			throw new IncorrectDistributionParameterException("Remember: the number of degrees of freedom must be an integer gtz");
		}
	}

	/**
	 * it returns the mean of the distribution.
	 * This method is used to obtain from the distribution the value of his own
	 * theoretic mean.
	 *
	 * @param p parameter of the student T distribution.
	 * @throws IncorrectDistributionParameterException
	 * @return double with the theoretic mean of the distribution.
	 *
	 */
	// the mean of a student T distribution, however, is always 0.

	//OLD
    //public double theorMean(StudentTPar p)
    public double theorMean(Parameter p)
            throws IncorrectDistributionParameterException{
        //alternative implementation may use p.check()
		if (p.check()){
            return 0;
        } else {
            throw new IncorrectDistributionParameterException("");
        }
	}

	/**
	 * it returns the variance of the distribution.
	 * This method is used to obtain from the distribution his own theoretical
	 * variance.
	 *
	 * @param p parameter of the student T distribution.
	 * @throws IncorrectDistributionParameterException
	 * @return double with the theoretic variance of the distribution which
	 * is calculated as n/(n-2) which mean that it makes sense only if n>2; else,
	 * the variance will be assumed to be 0.
	 *
	 */

	//OLD
    //public double theorVariance(StudentTPar p)
    public double theorVariance(Parameter p)
	        throws IncorrectDistributionParameterException {
		if (p.check()) {
			//OLD
            //double freedom = p.getFreedom();
            double freedom = ((StudentTPar) p).getFreedom();
			if (freedom < 2)
				return 0;
			else
				return freedom / (freedom - 2);
		} else {
			throw new IncorrectDistributionParameterException("Remember: the number of degrees of freedom must be an integer gtz");
		}
	}

	/**
	 * it returns the new random number.
	 * This method is used to obtain from the distribution the next number distributed
	 * according to the distribution parameter.
	 *
	 * @param p parameter of the student T distribution.
	 * @throws IncorrectDistributionParameterException
	 * @return double with the next random number of this distribution.
	 */

    public double nextRand(Parameter p)
            throws IncorrectDistributionParameterException {
            if (p.check()) {
                double freedom = ((StudentTPar) p).getFreedom();
                double u,v,w;
                do {
                    u = 2.0 * engine.raw() - 1.0;
                    v = 2.0 * engine.raw() - 1.0;
                } while ((w = u * u + v * v) > 1.0);
                // If generated number is in the past, reruns this method
                double ret = (u * Math.sqrt(freedom * (Math.exp(-2.0 / freedom * Math.log(w)) - 1.0) / w));
                return (ret  > 0)? ret : nextRand(p);
            } else {
                throw new IncorrectDistributionParameterException("Remember: the number of degrees of freedom must be an integer gtz");
            }
    }


} // end StudentT