/* *
* Title:
* Description:
* Copyright: Copyright (c)
* Company:
* @author
* @version 1.0
*/
package umontreal.iro.lecuyer.probdist;
import umontreal.iro.lecuyer.util.*;
import umontreal.iro.lecuyer.functions.MathFunction;
/**
* Extends the class {@link ContinuousDistribution} for
* the Nakagami distribution with location parameter a,
* scale parameter
* λ > 0 and shape parameter c > 0.
* The density is
*
*
*
* f (x) = 2λc/Γ(c) (x - a)2c-1 e-λ(x-a)2 for x > a,
*
*
*
*
* f (x) = 0 for x <= a,
*
* where Γ is the gamma function.
*
*/
public class NakagamiDist extends ContinuousDistribution {
protected double a; // Location parameter
protected double lambda; // Scale parameter
protected double c; // Shape parameter
private double factor;
private double ratio; // Gamma(c + 1/2)/Gamma(c)
/**
* Constructs a NakagamiDist object with parameters a =
* a, λ = lambda and c = c.
*
*/
public NakagamiDist (double a, double lambda, double c) {
setParams (a, lambda, c);
}
public double density (double x) {
if (x <= a) return 0.0;
return 2.0 * Math.exp( factor
+ Math.log(x-a)*(2.0*c-1.0)
- lambda*(x-a)*(x-a) );
}
public double cdf (double x) {
return cdf (a, lambda, c, x);
}
public double barF (double x) {
return barF (a, lambda, c, x);
}
public double inverseF (double u) {
return inverseF (a, lambda, c, u);
}
public double getMean() {
return a + ratio/Math.sqrt(lambda);
}
public double getVariance() {
return (c - ratio*ratio)/lambda;
}
public double getStandardDeviation() {
return Math.sqrt(getVariance ());
}
/**
* Computes the density function of the Nakagami distribution.
*
* @param a the location parameter
*
* @param lambda the scale parameter
*
* @param c the shape parameter
*
* @param x the value at which the density is evaluated
*
* @return returns the density function
*
*/
public static double density (double a, double lambda, double c,
double x) {
if (lambda <= 0.0)
throw new IllegalArgumentException ("lambda <= 0");
if (c <= 0.0)
throw new IllegalArgumentException ("c <= 0");
if (x <= a)
return 0.0;
return 2.0 * Math.exp( Math.log(lambda)*c - Num.lnGamma(c)
+ Math.log(x-a)*(2.0*c-1.0)
- lambda*(x-a)*(x-a) );
}
/**
* Computes the distribution function.
*
* @param a the location parameter
*
* @param lambda the scale parameter
*
* @param c the shape parameter
*
* @param x the value at which the distribution is evaluated
*
* @return returns the cdf function
*
*/
public static double cdf (double a, double lambda, double c, double x) {
if (lambda <= 0.0)
throw new IllegalArgumentException ("lambda <= 0");
if (c <= 0.0)
throw new IllegalArgumentException ("c <= 0");
if (x <= a)
return 0.0;
return GammaDist.cdf(c, 12, lambda*(x-a)*(x-a));
}
/**
* Computes the complementary distribution function.
*
* @param a the location parameter
*
* @param lambda the scale parameter
*
* @param c the shape parameter
*
* @param x the value at which the complementary distribution is evaluated
*
* @return returns the complementary distribution function
*
*/
public static double barF (double a, double lambda, double c, double x) {
if (lambda <= 0.0)
throw new IllegalArgumentException ("lambda <= 0");
if (c <= 0.0)
throw new IllegalArgumentException ("c <= 0");
if (x <= a)
return 1.0;
return GammaDist.barF(c, 12, lambda*(x-a)*(x-a));
}
/**
* Computes the inverse of the distribution function.
*
* @param a the location parameter
*
* @param lambda the scale parameter
*
* @param c the shape parameter
*
* @param u the value at which the inverse distribution is evaluated
*
* @return returns the inverse distribution function
*
*/
public static double inverseF (double a, double lambda, double c,
double u) {
if (lambda <= 0.0)
throw new IllegalArgumentException ("lambda <= 0");
if (c <= 0.0)
throw new IllegalArgumentException ("c <= 0");
if (u > 1.0 || u < 0.0)
throw new IllegalArgumentException ("u not in [0,1]");
if (u <= 0.0) return a;
if (u >= 1.0)
return Double.POSITIVE_INFINITY;
double res = GammaDist.inverseF(c, 12, u);
return a + Math.sqrt(res/lambda);
}
/**
* .
*
* Computes and returns the mean
*
*
*
* E[X] = a + 
.
*
*
* @param a the location parameter
*
* @param lambda the scale parameter
*
* @param c the shape parameter
*
* @return returns the mean
*
*/
public static double getMean (double a, double lambda, double c) {
if (lambda <= 0.0)
throw new IllegalArgumentException ("lambda <= 0");
if (c <= 0.0)
throw new IllegalArgumentException ("c <= 0");
return a + Num.gammaRatioHalf(c) / Math.sqrt(lambda);
}
/**
* .
*
* Computes and returns the variance
*
*
*
* Var[X] = 
[c - ([tex2html_wrap_indisplay261])2].
*
*
* @param a the location parameter
*
* @param lambda the scale parameter
*
* @param c the shape parameter
*
* @return returns the variance
*
*/
public static double getVariance (double a, double lambda, double c) {
if (lambda <= 0.0)
throw new IllegalArgumentException ("lambda <= 0");
if (c <= 0.0)
throw new IllegalArgumentException ("c <= 0");
double rat = Num.gammaRatioHalf(c);
return (c - rat*rat) / lambda;
}
/**
* Computes the standard deviation of the Nakagami distribution with
* parameters a, λ and c.
*
* @param a the location parameter
*
* @param lambda the scale parameter
*
* @param c the shape parameter
*
* @return returns the standard deviation
*
*/
public static double getStandardDeviation (double a, double lambda,
double c) {
return Math.sqrt (NakagamiDist.getVariance (a, lambda, c));
}
/**
* Returns the location parameter a of this object.
*
* @return returns the location parameter
*
*/
public double getA() {
return a;
}
/**
* Returns the scale parameter λ of this object.
*
* @return returns the scale parameter
*
*/
public double getLambda() {
return lambda;
}
/**
* Returns the shape parameter c of this object.
*
* @return returns the shape parameter
*
*/
public double getC() {
return c;
}
/**
* Sets the parameters a, λ and c of this object.
*
* @param a the location parameter
*
* @param lambda the scale parameter
*
* @param c the shape parameter
*
*
*/
public void setParams (double a, double lambda, double c) {
if (lambda <= 0.0)
throw new IllegalArgumentException ("lambda <= 0");
if (c <= 0.0)
throw new IllegalArgumentException ("c <= 0");
this.a = a;
this.lambda = lambda;
this.c = c;
factor = (Math.log(lambda)*c - Num.lnGamma(c));
ratio = Num.gammaRatioHalf(c);
}
/**
* Return a table containing the parameters of the current distribution.
* This table is put in regular order: [a, λ, c].
*
* @return returns the parameters [a, λ, c]
*
*/
public double[] getParams () {
double[] retour = {a, lambda, c};
return retour;
}
/**
* Returns a String containing information about the current distribution.
*
* @return returns a String containing information about the current distribution.
*
*/
public String toString () {
return getClass().getSimpleName() + " : a = " + a + ", lambda = " + lambda
+ ", c = " + c;
}
}