SSJ
V. labo.

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

FisherFDist

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)
          .
 
Method Summary
 double barF(double x)
          Returns the complementary distribution function.
static double barF(int n1, int n2, double x)
          .
static double barF(int n1, int n2, int d, double x)
          Deprecated. 
 double cdf(double x)
          .
static double cdf(int n1, int n2, double 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)
          .
 int getM()
          Deprecated. 
 double getMean()
          Returns the mean.
static double getMean(int n1, int n2)
          .
 int getN()
          Deprecated. 
 int getN1()
          [tabb90]
 int getN2()
          .
 double[] getParams()
          .
 double getStandardDeviation()
          Returns the standard deviation.
static double getStandardDeviation(int n1, int n2)
          .
 double getVariance()
          Returns the variance.
static double getVariance(int n1, int n2)
          .
 double inverseF(double u)
          Returns the inverse distribution function x = F-1(u).
static double inverseF(int n1, int n2, double u)
          .
static double inverseF(int n1, int n2, int d, double u)
          Deprecated. 
 void setParams(int n1, int n2)
          .
 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)
. \begin{tabb}
 Constructs a Fisher $F$\ distribution with \texttt{n1} and \texttt{n2} degrees of freedom.
 \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 n1,
                             int n2,
                             double x)
. \begin{tabb}Computes the density function for a Fisher
 $F$\ distribution with \texttt{n1} and \texttt{n2} degrees of freedom,
 evaluated at $x$.
 \end{tabb}

 


cdf

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

. \begin{hide}
 \par
 \begin{tabb}
 Computes the distribution function of the Fisher ...
 ...ted at $x$, with roughly $d$
 decimal digits of precision.
 \end{tabb}\end{hide}


cdf

public static double cdf(int n1,
                         int n2,
                         double x)
. \begin{tabb}
 Computes the distribution function of the Fisher $F$\ distribution with
 parameters \texttt{n1} and \texttt{n2}, evaluated at $x$.
 \end{tabb}

 


barF

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

. \begin{hide}
 \par
 \begin{tabb}
 Computes the complementary distribution function ...
 ...ted at $x$, with roughly
 $d$\ decimal digits of precision.
 \end{tabb}\end{hide}


barF

public static double barF(int n1,
                          int n2,
                          double x)
. \begin{tabb}
 Computes the complementary distribution function of the Fisher $F$\...
 ...bution
 with parameters \texttt{n1} and \texttt{n2}, evaluated at $x$.
 \end{tabb}

 


inverseF

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

. \begin{hide}
 \par
 \begin{tabb}
 Computes the inverse of the Fisher $F$\ distribut...
 ...ted at $u$, with roughly $d$\ decimal digits of
 precision.
 \end{tabb}\end{hide}


inverseF

public static double inverseF(int n1,
                              int n2,
                              double u)
. \begin{tabb}
 Computes the inverse of the Fisher $F$\ distribution with parameters \texttt{n1}
 and \texttt{n2}, evaluated at $u$.
 \end{tabb}


getMean

public static double getMean(int n1,
                             int n2)
. \begin{tabb}Computes and returns the mean $E[X] = n_2 / (n_2 - 2)$\ of the
 Fisher $F$\ distribution with parameters \texttt{n1} and \texttt{n2} $=n_2$.
 \end{tabb}
the mean of the Fisher F distribution


getVariance

public static double getVariance(int n1,
                                 int n2)
. \begin{tabb}Computes and returns the variance
 of the Fisher $F$\ distribution with parameters \texttt{n1} $=n_1$
 and \texttt{n2} $=n_2$.
 \end{tabb}
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)
. \begin{tabb}Computes and returns the standard deviation
 of the Fisher $F$\ distribution with parameters \texttt{n1} and \texttt{n2}.
 \end{tabb}
the standard deviation of the Fisher F distribution
 


getN

@Deprecated
public int getN()
Deprecated. 

. \begin{tabb}Returns the parameter \texttt{n1} of this object.
 \end{tabb}


getM

@Deprecated
public int getM()
Deprecated. 

. \begin{hide}
 \par
 \begin{tabb}Returns the parameter \texttt{n2} of this object.
 \end{tabb}\end{hide}


getN1

public int getN1()
[tabb90]


getN2

public int getN2()
. \begin{tabb}Returns the parameter \texttt{n2} of this object.
 \end{tabb}


setParams

public void setParams(int n1,
                      int n2)
. \begin{tabb}
 Sets the parameters \texttt{n1} and \texttt{n2} of this object.
 \end{tabb}


getParams

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