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## 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 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)nn/2mm/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
`FisherFDist(int n, int m)` Constructs a Fisher F distribution with n and m degrees of freedom.

Method Summary
`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)` Computes and returns the inverse distribution function x = F-1(u), by calling the method `inverseBrent`.
`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.
`String` | `toString()`

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
`inverseBisection, inverseBrent`

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), which is not accurate when F(x) -> 1.

  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`
  Computes and returns the inverse distribution function x = F-1(u), by calling the method `inverseBrent`. 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 String toString()

  Overrides:
    `toString` in class `Object`

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