Extends the class ContinuousDistribution for the Kolmogorov-Smirnov distribution with parameter \(n\). More...

Inheritance diagram for umontreal.ssj.probdist.KolmogorovSmirnovDist:

Public Member Functions
	KolmogorovSmirnovDist (int n)
	Constructs a Kolmogorov–Smirnov distribution with parameter.
double	density (double x)
	Returns \(f(x)\), the density evaluated at \(x\).
double	cdf (double x)
	Returns the distribution function \(F(x)\).
double	barF (double x)
	Returns the complementary distribution function.
double	inverseF (double u)
	Returns the inverse distribution function \(x = F^{-1}(u)\).
int	getN ()
	Returns the parameter \(n\) of this object.
void	setN (int n)
	Sets the parameter \(n\) of this object.
double[]	getParams ()
	Returns an array containing the parameter \(n\) of this object.
String	toString ()
	Returns a String containing information about the current distribution.
Public Member Functions inherited from umontreal.ssj.probdist.ContinuousDistribution
double	inverseBrent (double a, double b, double u, double tol)
	Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method.
double	inverseBisection (double u)
	Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection.
double	getMean ()
	Returns the mean.
double	getVariance ()
	Returns the variance.
double	getStandardDeviation ()
	Returns the standard deviation.
double	getXinf ()
	Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
double	getXsup ()
	Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
void	setXinf (double xa)
	Sets the value \(x_a=\) xa, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
void	setXsup (double xb)
	Sets the value \(x_b=\) xb, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).

Static Public Member Functions
static double	density (int n, double x)
	Computes the density for the Kolmogorov–Smirnov distribution with parameter \(n\).
static double	cdf (int n, double x)
	Computes the Kolmogorov–Smirnov distribution function \(F(x)\) with parameter \(n\) using Durbin’s matrix formula [54] .
static double	barF (int n, double x)
	Computes the complementary distribution function \(\bar{F}(x)\) with parameter \(n\).
static double	inverseF (int n, double u)
	Computes the inverse \(x = F^{-1}(u)\) of the Kolmogorov–Smirnov distribution \(F(x)\) with parameter \(n\).

Detailed Description

Extends the class ContinuousDistribution for the Kolmogorov-Smirnov distribution with parameter \(n\).

[54] . Given an empirical distribution \(F_n\) with \(n\) independent observations and a continuous distribution \(F(x)\), the two-sided Kolmogorov–Smirnov statistic is defined as

\[ D_n = \sup_{-\infty\le x \le\infty} |F_n(x) - F(x)| = \max\{D_n^+, D_n^-\}, \]

where \(D_n^+\) and \(D_n^-\) are the Kolmogorov–Smirnov+ and Kolmogorov–Smirnov \(-\) statistics as defined in equations DNp and DNm of this guide. This class implements a high precision version of the Kolmogorov–Smirnov distribution \(P[D_n \le x]\); it is a Java translation of the \(C\) program written in [171] . According to its authors, it should give 13 decimal digits of precision. It is extremely slow for large values of \(n\).

Definition at line 52 of file KolmogorovSmirnovDist.java.

Constructor & Destructor Documentation

◆ KolmogorovSmirnovDist()

umontreal.ssj.probdist.KolmogorovSmirnovDist.KolmogorovSmirnovDist ( int n )

Constructs a Kolmogorov–Smirnov distribution with parameter.

\(n\). Restriction: \(n \ge1\).

Definition at line 82 of file KolmogorovSmirnovDist.java.

Member Function Documentation

◆ barF() [1/2]

double umontreal.ssj.probdist.KolmogorovSmirnovDist.barF ( double x )

Returns the complementary distribution function.

The default implementation computes \(\bar{F}(x) = 1 - F(x)\).

Parameters

x	value at which the complementary distribution function is evaluated

Returns: complementary distribution function evaluated at x

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Reimplemented in umontreal.ssj.probdist.KolmogorovSmirnovDistQuick.

Definition at line 94 of file KolmogorovSmirnovDist.java.

◆ barF() [2/2]

double umontreal.ssj.probdist.KolmogorovSmirnovDist.barF	(	int	n,
		double	x )

static

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.

Reimplemented in umontreal.ssj.probdist.KolmogorovSmirnovDistQuick.

Definition at line 351 of file KolmogorovSmirnovDist.java.

◆ cdf() [1/2]

double umontreal.ssj.probdist.KolmogorovSmirnovDist.cdf ( double x )

Returns the distribution function \(F(x)\).

Parameters

x	value at which the distribution function is evaluated

Returns: distribution function evaluated at x

Implements umontreal.ssj.probdist.Distribution.

Reimplemented in umontreal.ssj.probdist.KolmogorovSmirnovDistQuick.

Definition at line 90 of file KolmogorovSmirnovDist.java.

◆ cdf() [2/2]

double umontreal.ssj.probdist.KolmogorovSmirnovDist.cdf	(	int	n,
		double	x )

static

Computes the Kolmogorov–Smirnov distribution function \(F(x)\) with parameter \(n\) using Durbin’s matrix formula [54] .

It is a translation of the \(C\) program in [171] ; according to its authors, it returns 13 decimal digits of precision. It is extremely slow for large \(n\).

Reimplemented in umontreal.ssj.probdist.KolmogorovSmirnovDistQuick.

Definition at line 310 of file KolmogorovSmirnovDist.java.