Documentation of 'umontreal.iro.lecuyer.probdist.AndersonDarlingDist' Java class
AndersonDarlingDist
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umontreal.iro.lecuyer.probdist

Class AndersonDarlingDist

  • All Implemented Interfaces:
    Distribution
    Direct Known Subclasses:
    AndersonDarlingDistQuick

    public class AndersonDarlingDist
extends ContinuousDistribution
    Extends the class ContinuousDistribution for the Anderson-Darling distribution (see). Given a sample of n independent uniforms Ui over (0, 1), the Anderson-Darling statistic An2 is defined by

    An2 = - n - 1/n∑j=1n{(2j - 1)ln(U(j)) + (2n + 1 - 2j)ln(1 - U(j))},

    where the U(j) are the Ui sorted in increasing order. The distribution function (the cumulative probabilities) is defined as Fn(x) = P[An2 <= x].

    • Constructor Summary

      Constructors 
      Constructor and Description
      AndersonDarlingDist(int n)
      Constructs an Anderson-Darling distribution for a sample of size n.

    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method and Description
      double barF(double x)
      Returns the complementary distribution function.
      static double barF(int n, double x)
      Computes the complementary distribution function bar(F)n(x) with parameter n.
      double cdf(double x)
      Returns the distribution function F(x).
      static double cdf(int n, double x)
      Computes the Anderson-Darling distribution function Fn(x), with parameter n, using Marsaglia's and al.
      double density(double x)
      Returns f (x), the density evaluated at x.
      static double density(int n, double x)
      Computes the density of the Anderson-Darling distribution with parameter n.
      int getN()
      Returns the parameter n of this object.
      double[] getParams()
      Return an array containing the parameter n of the current distribution.
      double inverseF(double u)
      Returns the inverse distribution function x = F-1(u).
      static double inverseF(int n, double u)
      Computes the inverse x = Fn-1(u) of the Anderson-Darling distribution with parameter n.
      void setN(int n)
      Sets the parameter n of this object.
      java.lang.String toString() 

      • Methods inherited from class java.lang.Object

        equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

    • Constructor Detail

      • AndersonDarlingDist

        public AndersonDarlingDist(int n)
        Constructs an Anderson-Darling distribution for a sample of size n.

    • Method Detail

      • density

        public double density(double x)
        Description copied from class: ContinuousDistribution
        Returns f (x), the density evaluated at x.
        Specified by:
        density in class ContinuousDistribution
        Parameters:
        x - value at which the density is evaluated
        Returns:
        density function evaluated at x

      • cdf

        public double cdf(double x)
        Description copied from interface: Distribution
        Returns the distribution function F(x).
        Parameters:
        x - value at which the distribution function is evaluated
        Returns:
        distribution function evaluated at x

      • barF

        public double barF(double x)
        Description copied from class: ContinuousDistribution
        Returns the complementary distribution function. The default implementation computes bar(F)(x) = 1 - F(x).
        Specified by:
        barF in interface Distribution
        Overrides:
        barF in class ContinuousDistribution
        Parameters:
        x - value at which the complementary distribution function is evaluated
        Returns:
        complementary distribution function evaluated at x

      • inverseF

        public double inverseF(double u)
        Description copied from class: ContinuousDistribution
        Returns the inverse distribution function x = F-1(u). Restrictions: u∈[0, 1].
        Specified by:
        inverseF in interface Distribution
        Overrides:
        inverseF in class ContinuousDistribution
        Parameters:
        u - value at which the inverse distribution function is evaluated
        Returns:
        the inverse distribution function evaluated at u

      • density

        public static double density(int n,
                             double x)
        Computes the density of the Anderson-Darling distribution with parameter n.

      • cdf

        public static double cdf(int n,
                         double x)
        Computes the Anderson-Darling distribution function Fn(x), with parameter n, using Marsaglia's and al. algorithm. First the asymptotic distribution for n -> ∞ is computed. Then an empirical correction obtained by simulation is added for finite n.

      • barF

        public static double barF(int n,
                          double x)
        Computes the complementary distribution function bar(F)n(x) with parameter n.

      • inverseF

        public static double inverseF(int n,
                              double u)
        Computes the inverse x = Fn-1(u) of the Anderson-Darling distribution with parameter n.

      • getN

        public int getN()
        Returns the parameter n of this object.

      • setN

        public void setN(int n)
        Sets the parameter n of this object.

      • getParams

        public double[] getParams()
        Return an array containing the parameter n of the current distribution.

      • toString

        public java.lang.String toString()
        Overrides:
        toString in class java.lang.Object
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