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) = αδe^{δγ+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