FisherFDist (Java Libraries for Stochastic Simulation)

java.lang.Object
- umontreal.iro.lecuyer.probdist.ContinuousDistribution
- - umontreal.iro.lecuyer.probdist.FisherFDist

All Implemented Interfaces:

Distribution
```
public class FisherFDist
extends ContinuousDistribution
```
Extends the class ContinuousDistribution for the Fisher F distribution with n and m degrees of freedom, where n and m are positive integers. Its density is

f (x) = Γ((n + m)/2)n^n/2m^m/2/[Γ(n/2)Γ(m/2)]x^(n-2)/2/(m + nx)^(n+m)/2, for x > 0.
where Γ(x) is the gamma function defined in GammaDist.
The non-static versions of the methods cdf, barF, and inverseF call the static version of the same name.

Field Summary
- Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
  decPrec

Constructor Summary

Constructors
Constructor and Description

FisherFDist(int n, int m)
Constructs a Fisher F distribution with n and m degrees of freedom.

Constructors
Constructor and Description
`FisherFDist(int n, int m)` Constructs a Fisher F distribution with n and m degrees of freedom.

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`barF(double x)` Returns the complementary distribution function.
`static double`	`barF(int n, int m, int d, double x)` Computes the complementary distribution function of the Fisher F distribution with parameters n and m, evaluated at x, with roughly d decimal digits of precision.
`double`	`cdf(double x)` Returns the distribution function F(x).
`static double`	`cdf(int n, int m, int d, double x)` Computes the distribution function of the Fisher F distribution with parameters n and m, evaluated at x, with roughly d decimal digits of precision.
`double`	`density(double x)` Returns f (x), the density evaluated at x.
`static double`	`density(int n, int m, double x)` Computes the density function for a Fisher F distribution with n and m degrees of freedom.
`int`	`getM()` Returns the parameter m of this object.
`double`	`getMean()` Returns the mean.
`static double`	`getMean(int n, int m)` Computes and returns the mean E[X] = m/(m - 2) of the Fisher F distribution with parameters n and m.
`int`	`getN()` Returns the parameter n 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 n, int m)` Computes and returns the standard deviation of the Fisher F distribution with parameters n and m.
`double`	`getVariance()` Returns the variance.
`static double`	`getVariance(int n, int m)` Computes and returns the variance of the Fisher F distribution with parameters n and m.
`double`	`inverseF(double u)` Returns the inverse distribution function x = F^-1(u).
`static double`	`inverseF(int n, int m, int d, double u)` Computes the inverse of the Fisher F distribution with parameters n and m, evaluated at x, with roughly d decimal digits of precision.
`void`	`setParams(int n, int m)` Sets the parameters n and m of this object.
`java.lang.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 n,
           int m)
```
    Constructs a Fisher F distribution with n and m 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 n,
             int m,
             double x)
```
    Computes the density function for a Fisher F distribution with n and m degrees of freedom.
  - cdf
```
public static double cdf(int n,
         int m,
         int d,
         double x)
```
    Computes the distribution function of the Fisher F distribution with parameters n and m, evaluated at x, with roughly d decimal digits of precision.
  - barF
```
public static double barF(int n,
          int m,
          int d,
          double x)
```
    Computes the complementary distribution function of the Fisher F distribution with parameters n and m, evaluated at x, with roughly d decimal digits of precision.
  - inverseF
```
public static double inverseF(int n,
              int m,
              int d,
              double u)
```
    Computes the inverse of the Fisher F distribution with parameters n and m, evaluated at x, with roughly d decimal digits of precision.
  - getMean
```
public static double getMean(int n,
             int m)
```
    Computes and returns the mean E[X] = m/(m - 2) of the Fisher F distribution with parameters n and m.
    
    Returns:
    the mean of the Fisher F distribution
  - getVariance
```
public static double getVariance(int n,
                 int m)
```
    Computes and returns the variance of the Fisher F distribution with parameters n and m.
    
    Returns:
    the variance of the Fisher F distribution Var[X] = (2m²(m + n - 2))/(n(m - 2)²(m - 4))
  - getStandardDeviation
```
public static double getStandardDeviation(int n,
                          int m)
```
    Computes and returns the standard deviation of the Fisher F distribution with parameters n and m.
    
    Returns:
    the standard deviation of the Fisher F distribution
  - getN
```
public int getN()
```
    Returns the parameter n of this object.
  - getM
```
public int getM()
```
    Returns the parameter m of this object.
  - setParams
```
public void setParams(int n,
             int m)
```
    Sets the parameters n and m of this object.
  - getParams
```
public double[] getParams()
```
    Return a table containing the parameters of the current distribution. This table is put in regular order: [n, m].
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object

Class FisherFDist

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

Constructor Summary

Method Summary

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

Methods inherited from class java.lang.Object

Constructor Detail

FisherFDist

Method Detail

density

cdf

barF

inverseF

getMean

getVariance

getStandardDeviation

density

cdf

barF

inverseF

getMean

getVariance

getStandardDeviation

getN

getM

setParams

getParams

toString