SSJ
V. 2.6.

umontreal.iro.lecuyer.probdist
Class FisherFDist

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

public class FisherFDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the Fisher F distribution with n1 and n2 degrees of freedom, where n1 and n2 are positive integers. Its density is

f (x) = Γ((n1 + n2)/2)n1n1/2n2n2/2/[Γ(n1/2)Γ(n2/2)]x(n1-2)/2/(n2 + n1x)(n1+n2)/2,         for x > 0.

where Γ(x) is the gamma function defined in GammaDist.


Field Summary
 
Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
decPrec
 
Constructor Summary
FisherFDist(int n1, int n2)
          Constructs a Fisher F distribution with n1 and n2 degrees of freedom.
 
Method Summary
 double barF(double x)
          Returns the complementary distribution function.
static double barF(int n1, int n2, double x)
          Computes the complementary distribution function of the Fisher F distribution with parameters n1 and n2, evaluated at x.
static double barF(int n1, int n2, int d, double x)
          Deprecated. 
 double cdf(double x)
          Returns the distribution function F(x).
static double cdf(int n1, int n2, double x)
          Computes the distribution function of the Fisher F distribution with parameters n1 and n2, evaluated at x.
static double cdf(int n1, int n2, int d, double x)
          Deprecated. 
 double density(double x)
          Returns f (x), the density evaluated at x.
static double density(int n1, int n2, double x)
          Computes the density function for a Fisher F distribution with n1 and n2 degrees of freedom, evaluated at x.
 int getM()
          Deprecated. 
 double getMean()
          Returns the mean.
static double getMean(int n1, int n2)
          Computes and returns the mean E[X] = n2/(n2 - 2) of the Fisher F distribution with parameters n1 and n2 = n2.
 int getN()
          Deprecated. 
 int getN1()
          Returns the parameter n1 of this object.
 int getN2()
          Returns the parameter n2 of this object.
 double[] getParams()
          Return a table containing the parameters of the current distribution.
 double getStandardDeviation()
          Returns the standard deviation.
static double getStandardDeviation(int n1, int n2)
          Computes and returns the standard deviation of the Fisher F distribution with parameters n1 and n2.
 double getVariance()
          Returns the variance.
static double getVariance(int n1, int n2)
          Computes and returns the variance of the Fisher F distribution with parameters n1 = n1 and n2 = n2.
 double inverseF(double u)
          Returns the inverse distribution function x = F-1(u).
static double inverseF(int n1, int n2, double u)
          Computes the inverse of the Fisher F distribution with parameters n1 and n2, evaluated at u.
static double inverseF(int n1, int n2, int d, double u)
          Deprecated. 
 void setParams(int n1, int n2)
          Sets the parameters n1 and n2 of this object.
 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

FisherFDist

public FisherFDist(int n1,
                   int n2)
Constructs a Fisher F distribution with n1 and n2 degrees of freedom.

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

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 n1,
                             int n2,
                             double x)
Computes the density function for a Fisher F distribution with n1 and n2 degrees of freedom, evaluated at x.


cdf

@Deprecated
public static double cdf(int n1,
                                    int n2,
                                    int d,
                                    double x)
Deprecated. 


cdf

public static double cdf(int n1,
                         int n2,
                         double x)
Computes the distribution function of the Fisher F distribution with parameters n1 and n2, evaluated at x.


barF

@Deprecated
public static double barF(int n1,
                                     int n2,
                                     int d,
                                     double x)
Deprecated. 


barF

public static double barF(int n1,
                          int n2,
                          double x)
Computes the complementary distribution function of the Fisher F distribution with parameters n1 and n2, evaluated at x.


inverseF

@Deprecated
public static double inverseF(int n1,
                                         int n2,
                                         int d,
                                         double u)
Deprecated. 


inverseF

public static double inverseF(int n1,
                              int n2,
                              double u)
Computes the inverse of the Fisher F distribution with parameters n1 and n2, evaluated at u.


getMean

public static double getMean(int n1,
                             int n2)
Computes and returns the mean E[X] = n2/(n2 - 2) of the Fisher F distribution with parameters n1 and n2 = n2.

Returns:
the mean of the Fisher F distribution

getVariance

public static double getVariance(int n1,
                                 int n2)
Computes and returns the variance of the Fisher F distribution with parameters n1 = n1 and n2 = n2.

Returns:
the variance of the Fisher F distribution Var[X] = (2n22(n2 + n1 - 2))/(n1(n2 - 2)2(n2 - 4))

getStandardDeviation

public static double getStandardDeviation(int n1,
                                          int n2)
Computes and returns the standard deviation of the Fisher F distribution with parameters n1 and n2.

Returns:
the standard deviation of the Fisher F distribution

getN

@Deprecated
public int getN()
Deprecated. 

Returns the parameter n1 of this object.


getM

@Deprecated
public int getM()
Deprecated. 


getN1

public int getN1()
Returns the parameter n1 of this object.


getN2

public int getN2()
Returns the parameter n2 of this object.


setParams

public void setParams(int n1,
                      int n2)
Sets the parameters n1 and n2 of this object.


getParams

public double[] getParams()
Return a table containing the parameters of the current distribution. This table is put in regular order: [n1, n2].


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.