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## umontreal.iro.lecuyer.probdist
Class NormalInverseGaussianDist

    java.lang.Object
      umontreal.iro.lecuyer.probdist.ContinuousDistribution
          umontreal.iro.lecuyer.probdist.NormalInverseGaussianDist

All Implemented Interfaces:
  Distribution

    public class NormalInverseGaussianDist

extends ContinuousDistribution

Extends the class `ContinuousDistribution` for the normal inverse gaussian distribution with location parameter μ, scale parameter δ > 0, tail heavyness α > 0, and asymmetry parameter β such that 0 <= | β| < α. Its density is

f (x) = αδeδγ+β(x-μ)K1(α(δ^2 + (x - μ)^2)1/2)/π(δ^2 + (x - μ)^2)1/2,

where K1 is the modified Bessel function of the second kind of order 1, and γ = (α^2 - β^2)1/2.

The distribution function is given by

F(x) = ∫-∞xdtf (t),

Field Summary

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

Constructor Summary
`NormalInverseGaussianDist(double alpha, double beta, double mu, double delta)` Constructor for a normal inverse gaussian distribution with parameters α = `alpha`, β = `beta`, μ = `mu` and δ = `delta`.

Method Summary
`double` | `barF(double x)` Returns the complementary distribution function.
`static double` | `barF(double alpha, double beta, double mu, double delta, double x)` NOT IMPLEMENTED.
`double` | `cdf(double x)` Returns the distribution function F(x).
`static double` | `cdf(double alpha, double beta, double mu, double delta, double x)` NOT IMPLEMENTED.
`double` | `density(double x)` Returns f (x), the density evaluated at x.
`static double` | `density(double alpha, double beta, double mu, double delta, double x)` Computes the density function for the normal inverse gaussian distribution with parameters α, β, μ and δ, evaluated at x.
`double` | `getAlpha()` Returns the parameter α of this object.
`double` | `getBeta()` Returns the parameter β of this object.
`double` | `getDelta()` Returns the parameter δ of this object.
`static NormalInverseGaussianDist` | `getInstanceFromMLE(double[] x, int n)` NOT IMPLEMENTED.
`double` | `getMean()` Returns the mean.
`static double` | `getMean(double alpha, double beta, double mu, double delta)` Returns the mean E[X] = μ + δβ/γ of the normal inverse gaussian distribution with parameters α, β, μ and δ.
`static double[]` | `getMLE(double[] x, int n)` NOT IMPLEMENTED.
`double` | `getMu()` Returns the parameter μ of this object.
`double[]` | `getParams()` Returns a table containing the parameters of the current distribution.
`double` | `getStandardDeviation()` Returns the standard deviation.
`static double` | `getStandardDeviation(double alpha, double beta, double mu, double delta)` Computes and returns the standard deviation of the normal inverse gaussian distribution with parameters α, β, μ and δ.
`double` | `getVariance()` Returns the variance.
`static double` | `getVariance(double alpha, double beta, double mu, double delta)` Computes and returns the variance Var[X] = δα2/γ3 of the normal inverse gaussian distribution with parameters α, β, μ and δ.
`static double` | `inverseF(double alpha, double beta, double mu, double delta, double u)` NOT IMPLEMENTED.
`void` | `setParams(double alpha, double beta, double mu, double delta)` Sets the parameters α, β, μ and δ of this object.
`String` | `toString()`

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

Methods inherited from class java.lang.Object
`equals, getClass, hashCode, notify, notifyAll, wait, wait, wait`

Constructor Detail

### NormalInverseGaussianDist

    public NormalInverseGaussianDist(double alpha,
                                     double beta,
                                     double mu,
                                     double delta)

  Constructor for a normal inverse gaussian distribution with parameters α = `alpha`, β = `beta`, μ = `mu` and δ = `delta`.

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`

### 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(double alpha,
                                 double beta,
                                 double mu,
                                 double delta,
                                 double x)

  Computes the density function for the normal inverse gaussian distribution with parameters α, β, μ and δ, evaluated at x.

### cdf

    public static double cdf(double alpha,
                             double beta,
                             double mu,
                             double delta,
                             double x)

  NOT IMPLEMENTED. Computes the distribution function of the normal inverse gaussian distribution with parameters α, β, μ and δ, evaluated at x.

### barF

    public static double barF(double alpha,
                              double beta,
                              double mu,
                              double delta,
                              double x)

  NOT IMPLEMENTED. Computes the complementary distribution function of the normal inverse gaussian distribution with parameters α, β, μ and δ, evaluated at x.

### inverseF

    public static double inverseF(double alpha,
                                  double beta,
                                  double mu,
                                  double delta,
                                  double u)

  NOT IMPLEMENTED. Computes the inverse of the normal inverse gaussian distribution with parameters α, β, μ and δ.

### getMLE

    public static double[] getMLE(double[] x,
                                  int n)

  NOT IMPLEMENTED.

  Parameters:
    `x` - the list of observations used to evaluate parameters
    `n` - the number of observations used to evaluate parameters
  Returns:
    returns the parameters [ hat(α), hat(β), hat(μ), hat(δ)]

### getInstanceFromMLE

    public static NormalInverseGaussianDist getInstanceFromMLE(double[] x,
                                                               int n)

  NOT IMPLEMENTED.

  Parameters:
    `x` - the list of observations to use to evaluate parameters
    `n` - the number of observations to use to evaluate parameters

### getMean

    public static double getMean(double alpha,
                                 double beta,
                                 double mu,
                                 double delta)

  Returns the mean E[X] = μ + δβ/γ of the normal inverse gaussian distribution with parameters α, β, μ and δ.

  Returns:
    the mean of the normal inverse gaussian distribution E[X] = μ + δβ/γ

### getVariance

    public static double getVariance(double alpha,
                                     double beta,
                                     double mu,
                                     double delta)

  Computes and returns the variance Var[X] = δα2/γ3 of the normal inverse gaussian distribution with parameters α, β, μ and δ.

  Returns:
    the variance of the normal inverse gaussian distribution Var[X] = δα2/γ3

### getStandardDeviation

    public static double getStandardDeviation(double alpha,
                                              double beta,
                                              double mu,
                                              double delta)

  Computes and returns the standard deviation of the normal inverse gaussian distribution with parameters α, β, μ and δ.

  Returns:
    the standard deviation of the normal inverse gaussian distribution

### getAlpha

    public double getAlpha()

  Returns the parameter α of this object.

### getBeta

    public double getBeta()

  Returns the parameter β of this object.

### getMu

    public double getMu()

  Returns the parameter μ of this object.

### getDelta

    public double getDelta()

  Returns the parameter δ of this object.

### setParams

    public void setParams(double alpha,
                          double beta,
                          double mu,
                          double delta)

  Sets the parameters α, β, μ and δ of this object.

### getParams

    public double[] getParams()

  Returns a table containing the parameters of the current distribution. This table is put in regular order: [α, β, μ, δ].

### 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.