SSJ
V. 2.6.

umontreal.iro.lecuyer.probdist
Class NormalInverseGaussianDist

java.lang.Object
  extended by umontreal.iro.lecuyer.probdist.ContinuousDistribution
      extended by 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
getXinf, getXsup, inverseBisection, inverseBrent, inverseF, setXinf, setXsup
 
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).

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

SSJ
V. 2.6.

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