SSJ
V. 2.6.

umontreal.iro.lecuyer.probdist
Class KolmogorovSmirnovDist

java.lang.Object
  extended by umontreal.iro.lecuyer.probdist.ContinuousDistribution
      extended by 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 Fn with n independent observations and a continuous distribution F(x), the two-sided statistic is defined as

Dn = sup-∞ <= x <= ∞| Fn(x) - F(x)|  = {Dn+, Dn-},

where Dn+ and Dn- 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[Dn <= 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 extremely slow for large values of n.


Field Summary
 
Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
decPrec
 
Constructor Summary
KolmogorovSmirnovDist(int n)
          Constructs a distribution with parameter 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)(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.
 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. It is a translation of the C program in; according to its authors, it returns 13 decimal digits of precision. It is extremely 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 String toString()
Overrides:
toString in class Object

SSJ
V. 2.6.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.