Extends the class KolmogorovSmirnovDist for the Kolmogorov–Smirnov distribution. More...

Inheritance diagram for umontreal.ssj.probdist.KolmogorovSmirnovDistQuick:

Public Member Functions
	KolmogorovSmirnovDistQuick (int n)
	Constructs a Kolmogorov–Smirnov distribution with parameter \(n\).
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 \(x = F^{-1}(u)\).
Public Member Functions inherited from umontreal.ssj.probdist.KolmogorovSmirnovDist
	KolmogorovSmirnovDist (int n)
	Constructs a Kolmogorov–Smirnov distribution with parameter.
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 \(u = P[D_n \le x]\) with parameter \(n\), using the program described in.
static double	barF (int n, double x)
	Computes the complementary Kolmogorov–Smirnov distribution.
static double	inverseF (int n, double u)
	Computes the inverse \(x = F^{-1}(u)\) of the distribution.

Detailed Description

Extends the class KolmogorovSmirnovDist for the Kolmogorov–Smirnov distribution.

The methods of this class are much faster than those of class KolmogorovSmirnovDist.

Definition at line 39 of file KolmogorovSmirnovDistQuick.java.

Constructor & Destructor Documentation

◆ KolmogorovSmirnovDistQuick()

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

Constructs a Kolmogorov–Smirnov distribution with parameter \(n\).

Definition at line 68 of file KolmogorovSmirnovDistQuick.java.

Member Function Documentation

◆ barF() [1/2]

double umontreal.ssj.probdist.KolmogorovSmirnovDistQuick.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.KolmogorovSmirnovDist.

Definition at line 80 of file KolmogorovSmirnovDistQuick.java.

◆ barF() [2/2]

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

static

Computes the complementary Kolmogorov–Smirnov distribution.

\(P[D_n \ge x]\) with parameter \(n\), in a form that is more precise in the upper tail, using the program described in [208] . It returns at least 10 decimal digits of precision everywhere for all \(n \le500\), at least 6 decimal digits of precision for \(500 < n \le200000\), and a few correct decimal 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: \(n\ge1\).

Reimplemented from umontreal.ssj.probdist.KolmogorovSmirnovDist.

Definition at line 412 of file KolmogorovSmirnovDistQuick.java.

◆ cdf() [1/2]

double umontreal.ssj.probdist.KolmogorovSmirnovDistQuick.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

Reimplemented from umontreal.ssj.probdist.KolmogorovSmirnovDist.

Definition at line 76 of file KolmogorovSmirnovDistQuick.java.

◆ cdf() [2/2]

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

static

Computes the Kolmogorov–Smirnov distribution function \(u = P[D_n \le x]\) with parameter \(n\), using the program described in.

[208] . This method uses Pomeranz’s recursion algorithm and the Durbin matrix algorithm [27], [198], [171] for \(n \le500\), which returns at least 13 decimal digits of precision. It uses the Pelz-Good asymptotic expansion [196] in the central part of the range for \(n > 500\) and returns at least 7 decimal digits of precision everywhere for \(500 < n \le100000\). For \(n > 100000\), it returns at least 5 decimal digits of precision for all \(u > 10^{-16}\), and a few correct decimals when \(u \le10^{-16}\). This method is much faster than method cdf of KolmogorovSmirnovDist for moderate or large \(n\). Restriction: \(n\ge1\).

Reimplemented from umontreal.ssj.probdist.KolmogorovSmirnovDist.

Definition at line 379 of file KolmogorovSmirnovDistQuick.java.