umontreal.iro.lecuyer.probdist
Class AndersonDarlingDist

java.lang.Object
  umontreal.iro.lecuyer.probdist.ContinuousDistribution
      umontreal.iro.lecuyer.probdist.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 U_i over (0, 1), the Anderson-Darling statistic A_n² is defined by

A_n² = - n - 1/n∑_j=1ⁿ{(2j - 1)ln(U_(j)) + (2n + 1 - 2j)ln(1 - U_(j))},

where the U_(j) are the U_i sorted in increasing order. The distribution function (the cumulative probabilities) is defined as F_n(x) = P[A_n² <= x].

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

decPrec

Constructor Summary

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

Method Summary

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.
String	toString()

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

getMean, getStandardDeviation, getVariance, getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup

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 F_n(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 = F_n^-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 String toString()

Overrides:

toString in class Object