SSJ
V. 2.6.

umontreal.iro.lecuyer.probdist
Class WatsonGDist

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

public class WatsonGDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the Watson G distribution (see). Given a sample of n independent uniforms Ui over [0, 1], the G statistic is defined by

Gn = (n)1/2max1 <= j <= n{j/n - U(j) + bar(U)n -1/2}  
  = (n)1/2(Dn+ + bar(U)n - 1/2),  

where the U(j) are the Ui sorted in increasing order, bar(U)n is the average of the observations Ui, and Dn+ is the Kolmogorov-Smirnov+ statistic. The distribution function (the cumulative probabilities) is defined as Fn(x) = P[Gn <= x].


Field Summary
 
Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
decPrec
 
Constructor Summary
WatsonGDist(int n)
          Constructs a Watson 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 Watson G 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 function for a Watson G distribution with parameter n.
 int getN()
          Returns the parameter n of this object.
 double[] getParams()
          Return 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 x = Fn-1(u), where Fn is the Watson G 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

WatsonGDist

public WatsonGDist(int n)
Constructs a Watson 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 function for a Watson G distribution with parameter n.


cdf

public static double cdf(int n,
                         double x)
Computes the Watson G distribution function Fn(x), with parameter n. A cubic spline interpolation is used for the asymptotic distribution when n -> ∞, and an empirical correction of order 1/(n)1/2, obtained empirically from 107 simulation runs with n = 256 is then added. The absolute error is estimated to be less than 0.01, 0.005, 0.002, 0.0008, 0.0005, 0.0005, 0.0005 for n = 16, 32, 64, 128, 256, 512, 1024, respectively.


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 x = Fn-1(u), where Fn is the Watson G 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()
Return 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.