SSJ
V. 2.6.

## umontreal.iro.lecuyer.probdist Class FisherFDist

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

`public class FisherFDistextends 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.