Package pal.statistics

Class 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

    • Method Summary

      All Methods Static Methods Concrete Methods 
      Modifier and Type Method Description
      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