NormalInverseGaussianDist (Java Libraries for Stochastic Simulation)

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

Constructors
Constructor and Description
`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

Methods
Modifier and Type	Method and Description
`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.
`java.lang.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 java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object

Class NormalInverseGaussianDist

Field Summary

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

Constructor Summary

Method Summary

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

Methods inherited from class java.lang.Object

Constructor Detail

NormalInverseGaussianDist

Method Detail

density

cdf

barF

getMean

getVariance

getStandardDeviation

density

cdf

barF

inverseF

getMLE

getInstanceFromMLE

getMean

getVariance

getStandardDeviation

getAlpha

getBeta

getMu

getDelta

setParams

getParams

toString