pal.statistics
Class ParetoDistribution

java.lang.Object
  pal.statistics.ParetoDistribution

public class ParetoDistribution
extends java.lang.Object

Pareto distribution (scale-free distribution without characteristic length scale). Parameters: shape parameter k>0, scale parameter m>0 ("minimum income")

Version:

$Id: ParetoDistribution.java,v 1.2 2001/07/13 14:39:13 korbinian Exp $

Author:

Korbinian Strimmer

Constructor Summary

ParetoDistribution()

Method Summary

static double	cdf(double x, double k, double m) cumulative density function of the Pareto distribution
static double	mean(double k, double m) mean of the Pareto distribution
static double	moment(int n, double k, double m) moments E(X^n) of the Pareto distribution
static double	pdf(double x, double k, double m) probability density function of the Pareto distribution
static double	quantile(double p, double k, double m) quantile (inverse cumulative density function) of the Pareto distribution
static double	variance(double k, double m) variance of the Pareto distribution

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

ParetoDistribution

public ParetoDistribution()

Method Detail

pdf

public static double pdf(double x,
                         double k,
                         double m)

probability density function of the Pareto distribution

Parameters:

x - argument (>=m)

k - shape parameter (>0)

m - scale parameter (>0, "minimum income")

Returns:

pdf value

cdf

public static double cdf(double x,
                         double k,
                         double m)

cumulative density function of the Pareto distribution

Parameters:

x - argument (>=m)

k - shape parameter (>0)

m - scale parameter (>0, "minimum income")

Returns:

cdf value

quantile

public static double quantile(double p,
                              double k,
                              double m)

quantile (inverse cumulative density function) of the Pareto distribution

Parameters:

p - argument (0 < p < 1)

k - shape parameter (>0)

m - scale parameter (>0, "minimum income")

Returns:

icdf value

mean

public static double mean(double k,
                          double m)

mean of the Pareto distribution

Parameters:

k - shape parameter (>0)

m - scale parameter (>0, "minimum income")

Returns:

mean

variance

public static double variance(double k,
                              double m)

variance of the Pareto distribution

Parameters:

k - shape parameter (>0)

m - scale parameter (>0, "minimum income")

Returns:

variance

moment

public static double moment(int n,
                            double k,
                            double m)

moments E(X^n) of the Pareto distribution

Parameters:

n - moment

k - shape parameter (>0)

m - scale parameter (>0, "minimum income")

Returns:

variance