erlang.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.Arithmetic;
import jmt.engine.math.Gamma;
import jmt.engine.random.engine.RandomEngine;


/**
 *
 * This is the Erlang distribution.
 *
 * <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
 */

public class Erlang extends Distribution {

	/**
	 * This is the constructor. It creates a new empty erlang.
	 * The erlang distribution is defined from is pdf:
	 * <pre>           (alpha^r)       (r-1)     (-alpha*x)
	 * pdf(x) = -------------  * x       * e
	 *           gammaFun(r)</pre>
	 * where r is the "shape" parameter, alpha is the "scale" parameter and
	 * gammaFun is the "Eulero" function.
	 */

	public Erlang() {
		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 erlang distribution.
	 * @throws IncorrectDistributionParameterException
	 * @return double with the probability distribution function evaluated in x.
	 */

	//OLD
    //public double pdf(double x, ErlangPar p)
    public double pdf(double x, Parameter p)
	        throws IncorrectDistributionParameterException {
		if (p.check()) {
			//OLD
            //double r = p.getR();
			//double alpha = p.getAlpha();
            double r = ((ErlangPar) p).getR();
			double alpha = ((ErlangPar) p).getAlpha();
			return (Math.pow(alpha, r) / Gamma.gamma(r)) * Math.pow(x, (r - 1)) * Math.exp(-alpha * x);
		} else {
			throw new IncorrectDistributionParameterException("Remember: alpha and r must be 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 erlang distribution.
	 * @throws IncorrectDistributionParameterException
	 * @return double with the cumulative distribution function evaluated in x.
	 */

	//OLD
    //public double cdf(double x, ErlangPar p)
    public double cdf(double x, Parameter p)
	        throws IncorrectDistributionParameterException {
		if (p.check()) {
			//OLD
            //double r = p.getR();
			//double alpha = p.getAlpha();
			double r = ((ErlangPar) p).getR();
			double alpha = ((ErlangPar) p).getAlpha();
            double sum = 0;
			double a;  // var di servizio per calcolare la somma
			for (int i = 0; i < r - 1; i++) {
				a = Math.pow((alpha * x), i) / Arithmetic.factorial(i);
				sum = sum + a;
			}
			;
			return 1 - Math.exp(-alpha * x) * sum;
		} else {
			throw new IncorrectDistributionParameterException("Remember: alpha and r must be 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 erlang distribution.
	 * @throws IncorrectDistributionParameterException
	 * @return double with the theoretic mean of the distribution.
	 *
	 * The theoretic mean is calculated  as r/alpha.
	 */
	//OLD
    //public double theorMean(ErlangPar p)
    public double theorMean(Parameter p)
	        throws IncorrectDistributionParameterException {
		if (p.check()) {
			//OLD
            //double r = p.getR();
			//double alpha = p.getAlpha();
            double r = ((ErlangPar) p).getR();
			double alpha = ((ErlangPar) p).getAlpha();
			return r / alpha;
		} else {
			throw new IncorrectDistributionParameterException("Remember: alpha and r must be gtz");
		}
	}

	/**
	 * 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 erlang distribution.
	 * @throws IncorrectDistributionParameterException
	 * @return double with the theoretic variance of the distribution.
	 *
	 * The theoretic variance is calculated  as r/(alpha^2)
	 */

	//OLD
    //public double theorVariance(ErlangPar p)
    public double theorVariance(Parameter p)
	        throws IncorrectDistributionParameterException {
		if (p.check()) {
			//OLD
            //double r = p.getR();
			//double alpha = p.getAlpha();
            double r = ((ErlangPar) p).getR();
			double alpha = ((ErlangPar) p).getAlpha();
			return r / (alpha * alpha);
		} else {
			throw new IncorrectDistributionParameterException("Remember: alpha and r must be 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 erlang distribution.
	 * @throws IncorrectDistributionParameterException
	 * @return double with the next random number of this distribution.
	 */

	public double nextRand(Parameter p)
	        throws IncorrectDistributionParameterException {
		if (p.check()) {
			double alpha = ((ErlangPar) p).getAlpha();
			double r = ((ErlangPar) p).getR();
			double par = 1.0;
			for (int i = 0; i < r; i++) {
				par = par * engine.raw();
			}
			return (-1 / alpha) * (Math.log(par));
		} else {
			throw new IncorrectDistributionParameterException("Remember: alpha and r must be gtz");
		}
	}


} // end Erlang