umontreal.iro.lecuyer.probdist

Class KolmogorovSmirnovDist

java.lang.Object

umontreal.iro.lecuyer.probdist.ContinuousDistribution

umontreal.iro.lecuyer.probdist.KolmogorovSmirnovDist

All Implemented Interfaces:

Distribution

Direct Known Subclasses:

KolmogorovSmirnovDistQuick

public class KolmogorovSmirnovDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the Kolmogorov-Smirnov distribution with parameter n. Given an empirical distribution F_n with n independent observations and a continuous distribution F(x), the two-sided statistic is defined as

D_n = sup_{-∞ <= x <= ∞}| F_n(x) - F(x)| = {D_n⁺, D_n^-},

where D_n⁺ and D_n^- are the + and - statistics as defined in equations and on page of this guide. This class implements a high precision version of the distribution P[D_n <= x]; it is a Java translation of the C program written in. According to its authors, it should give 13 decimal digits of precision. It is astronomically slow for large values of n.

Field Summary

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

decPrec

Constructor Summary

Constructors

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

Method Summary

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)(x) with parameter n.
double	cdf(double x) Returns the distribution function F(x).
static double	cdf(int n, double x) Computes the distribution function F(x) with parameter n using Durbin's matrix formula.
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.
int	getN() Returns the parameter n of this object.
double[]	getParams() Returns an array containing the parameter n of this object.
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.
void	setN(int n) Sets the parameter n of this object.
java.lang.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

KolmogorovSmirnovDist

public KolmogorovSmirnovDist(int n)

Constructs a distribution with parameter n. Restriction: n >= 1.

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 for the distribution with parameter n.

cdf

public static double cdf(int n,
         double x)

Computes the distribution function F(x) with parameter n using Durbin's matrix formula. According to its authors, it returns 13 decimal digits of precision except far in the upper tail for n >= 100, where it returns 7 decimal digits. It is astronomically slow for large n.

barF

public static double barF(int n,
          double x)

Computes the complementary distribution function bar(F)(x) with parameter n. Simply returns 1 - cdf(n,x). It is not precise in the upper tail.

inverseF

public static double inverseF(int n,
              double u)

Computes the inverse x = F^-1(u) of the distribution F(x) 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()

Returns an array containing the parameter n of this object.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object