SSJ
V. 2.6.

umontreal.iro.lecuyer.probdist
Class KolmogorovSmirnovPlusDist

java.lang.Object
  extended by umontreal.iro.lecuyer.probdist.ContinuousDistribution
      extended by umontreal.iro.lecuyer.probdist.KolmogorovSmirnovPlusDist
All Implemented Interfaces:
Distribution

public class KolmogorovSmirnovPlusDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the Kolmogorov-Smirnov+ distribution (see). Given a sample of n independent uniforms Ui over [0, 1], the Kolmogorov-Smirnov+ statistic Dn+ and the Kolmogorov-Smirnov- statistic Dn-, are defined by

Dn+ = max1 <= j <= n(j/n - U(j)),  
Dn- = max1 <= j <= n(U(j) - (j - 1)/n),  

where the U(j) are the Ui sorted in increasing order. Both statistics follows the same distribution function, i.e. Fn(x) = P[Dn+ <= x] = P[Dn- <= x].


Field Summary
 
Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
decPrec
 
Constructor Summary
KolmogorovSmirnovPlusDist(int n)
          Constructs an Kolmogorov-Smirnov+ distribution for a sample of size 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)n(x) with parameter n.
 double cdf(double x)
          Returns the distribution function F(x).
static double cdf(int n, double x)
          Computes the Kolmogorov-Smirnov+ distribution function Fn(x) with parameter n.
 double density(double x)
          Returns f (x), the density evaluated at x.
static double density(int n, double x)
          Computes the density of the Kolmogorov-Smirnov+ 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 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

KolmogorovSmirnovPlusDist

public KolmogorovSmirnovPlusDist(int n)
Constructs an Kolmogorov-Smirnov+ distribution for a sample of size n.

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 of the Kolmogorov-Smirnov+ distribution with parameter n.


cdf

public static double cdf(int n,
                         double x)
Computes the Kolmogorov-Smirnov+ distribution function Fn(x) with parameter n. The relative error on Fn(x) = P[Dn+ <= x] is always less than 10-5.


barF

public static double barF(int n,
                          double x)
Computes the complementary distribution function bar(F)n(x) with parameter n.


inverseF

public static double inverseF(int n,
                              double u)
Computes the inverse x = F-1(u) of the distribution 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.