umontreal.iro.lecuyer.probdist

Class KolmogorovSmirnovDistQuick

java.lang.Object

umontreal.iro.lecuyer.probdist.ContinuousDistribution

umontreal.iro.lecuyer.probdist.KolmogorovSmirnovDist

umontreal.iro.lecuyer.probdist.KolmogorovSmirnovDistQuick

All Implemented Interfaces:

Distribution

public class KolmogorovSmirnovDistQuick
extends KolmogorovSmirnovDist

Extends the class KolmogorovSmirnovDist for the distribution. The methods of this class are much faster than those of class KolmogorovSmirnovDist.

Field Summary

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

decPrec

Constructor Summary

Constructors

Constructor and Description
KolmogorovSmirnovDistQuick(int n) Constructs a distribution with parameter n.

Method Summary

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 P[Dn >= x] with parameter n, in a form that is more precise in the upper tail, using the program described in.
double	cdf(double x) Returns the distribution function F(x).
static double	cdf(int n, double x) Computes the distribution function u = P[Dn <= x] with parameter n, using the program described in.
double	density(double x) Returns f (x), the density evaluated at x.
static double	density(int n, double x) Computes the density for the distribution with parameter n.
double	inverseF(double u) Returns the inverse distribution function x = F-1(u).
static double	inverseF(int n, double u) Computes the inverse x = F-1(u) of the distribution F(x) with parameter n.

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

getN, getParams, setN, 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

KolmogorovSmirnovDistQuick

public KolmogorovSmirnovDistQuick(int n)

Constructs a distribution with parameter n.

Method Detail

density

public double density(double x)

Description copied from class: ContinuousDistribution

Returns f (x), the density evaluated at x.

Overrides:

density in class KolmogorovSmirnovDist

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).

Specified by:

cdf in interface Distribution

Overrides:

cdf in class KolmogorovSmirnovDist

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 KolmogorovSmirnovDist

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 KolmogorovSmirnovDist

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 for the distribution with parameter n.

cdf

public static double cdf(int n,
                         double x)

Computes the distribution function u = P[D_n <= x] with parameter n, using the program described in. This method uses Pomeranz's recursion algorithm and the Durbin matrix algorithm for n <= 140, which returns at least 13 decimal digits of precision. It uses the Pelz-Good asymptotic expansion in the central part of the range for n > 140 and returns at least 5 decimal digits of precision everywhere for 140 < n <= 100000. For n > 100000, it returns at least 5 decimal digits of precision for all u > 10^-16, and a few correct decimals when u <= 10^-16. For a given n > 140, the precision increases as x increases. This method is much faster than method cdf of KolmogorovSmirnovDist for moderate or large n. Restriction: n >= 1.

barF

public static double barF(int n,
                          double x)

Computes the complementary distribution P[D_n >= x] with parameter n, in a form that is more precise in the upper tail, using the program described in. It returns at least 10 decimal digits of precision everywhere for all n <= 140, at least 5 decimal digits of precision for 140 < n <= 200000, and a few correct digits (1 to 5) for n > 200000. This method is much faster and more precise for x close to 1, than method barF of KolmogorovSmirnovDist for moderate or large n. Restriction: n >= 1.

inverseF

public static double inverseF(int n,
                              double u)

Computes the inverse x = F^-1(u) of the distribution F(x) with parameter n.