SSJ
V. labo.

umontreal.iro.lecuyer.probdist
Class CramerVonMisesDist

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

public class CramerVonMisesDist
extends ContinuousDistribution

CramerVonMisesDist

Extends the class ContinuousDistribution for the Cramér-von Mises distribution (see[#!tDUR73a!#,#!tSTE70a!#,#!tSTE86b!#]). Given a sample of n independent uniforms Ui over [0, 1], the Cramér-von Mises statistic Wn2 is defined by

Wn2 = 1/12n + $\displaystyle \htsum_{{j=1}}^{n}$(U(j) - (j-0.5)/n)2,

where the U(j) are the Ui sorted in increasing order. The distribution function (the cumulative probabilities) is defined as Fn(x) = P[Wn2x].


Field Summary
 
Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
decPrec
 
Constructor Summary
CramerVonMisesDist(int n)
          .
 
Method Summary
 double barF(double x)
          Returns the complementary distribution function.
static double barF(int n, double x)
          .
 double cdf(double x)
          .
static double cdf(int n, double x)
          .
 double density(double x)
          Returns f (x), the density evaluated at x.
static double density(int n, double x)
          .
 double getMean()
          Returns the mean.
static double getMean(int n)
          .
 int getN()
          .
 double[] getParams()
          .
 double getStandardDeviation()
          Returns the standard deviation.
static double getStandardDeviation(int n)
          .
 double getVariance()
          Returns the variance.
static double getVariance(int n)
          .
 double inverseF(double u)
          Returns the inverse distribution function x = F-1(u).
static double inverseF(int n, double u)
          .
 void setN(int n)
          .
 String toString()
          .
 
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup
 
Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, wait, wait, wait
 

Constructor Detail

CramerVonMisesDist

public CramerVonMisesDist(int n)
. \begin{tabb}
 Constructs a {\em Cram\'er-von Mises\/} distribution for a sample of size $n$.
 \end{tabb}

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
. \begin{tabb}Returns the distribution function $F(x)$.
 \end{tabb}
xvalue at which the distribution function is evaluated 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

getMean

public double getMean()
Description copied from class: ContinuousDistribution
Returns the mean.

Specified by:
getMean in interface Distribution
Overrides:
getMean in class ContinuousDistribution
Returns:
the mean

getVariance

public double getVariance()
Description copied from class: ContinuousDistribution
Returns the variance.

Specified by:
getVariance in interface Distribution
Overrides:
getVariance in class ContinuousDistribution
Returns:
the variance

getStandardDeviation

public double getStandardDeviation()
Description copied from class: ContinuousDistribution
Returns the standard deviation.

Specified by:
getStandardDeviation in interface Distribution
Overrides:
getStandardDeviation in class ContinuousDistribution
Returns:
the standard deviation

density

public static double density(int n,
                             double x)
. \begin{tabb}Computes the density function
 for a {\em Cram\'er-von Mises\/} distribution with parameter $n$.
 \end{tabb}


cdf

public static double cdf(int n,
                         double x)
. \begin{tabb}
 Computes the Cram\'er-von Mises distribution function with paramet...
 ...n:
 $P(W_1^2 \le x) = 2 \sqrt {x - 1/12}$\ for $1/12 \le x \le 1/3$.
 \end{tabb}


barF

public static double barF(int n,
                          double x)
. \begin{tabb}
 Computes the complementary distribution function $\bar F_n(x)$
 with parameter $n$.
 \end{tabb}


inverseF

public static double inverseF(int n,
                              double u)
. \begin{tabb}
 Computes $x = F_n^{-1}(u)$, where $F_n$\ is the
 {\em Cram\'er-von Mises\/} distribution with parameter $n$.
 \end{tabb}


getMean

public static double getMean(int n)
. \begin{tabb}Returns the mean of the distribution with parameter $n$.
 \end{tabb}
the mean


getVariance

public static double getVariance(int n)
. \begin{tabb}Returns the variance of the distribution with parameter $n$.
 \end{tabb}
variance


getStandardDeviation

public static double getStandardDeviation(int n)
. \begin{tabb}Returns the standard deviation of the distribution with
 parameter $n$.
 \end{tabb}
the standard deviation


getN

public int getN()
. \begin{tabb}Returns the parameter $n$\ of this object.
 \end{tabb}


setN

public void setN(int n)
. \begin{tabb}Sets the parameter $n$\ of this object.
 \end{tabb}


getParams

public double[] getParams()
. \begin{tabb}
 Return an array containing the parameter $n$\ of this object.
 \end{tabb}

 


toString

public String toString()
. \begin{hide}
 \par
 \begin{tabb}
 Returns a \texttt{String} containing information about the current distribution.
 \end{tabb}\end{hide}

Overrides:
toString in class Object

SSJ
V. labo.

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