SSJ  3.3.1
Stochastic Simulation in Java
Public Member Functions | Static Public Member Functions | Protected Attributes | List of all members
NormalInverseGaussianDist Class Reference

Extends the class ContinuousDistribution for the normal inverse gaussian distribution with location parameter \(\mu\), scale parameter \(\delta> 0\), tail heavyness \(\alpha> 0\), and asymmetry parameter \(\beta\) such that \(0 \le|\beta| < \alpha\). More...

Inheritance diagram for NormalInverseGaussianDist:
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Collaboration diagram for NormalInverseGaussianDist:
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Public Member Functions

 NormalInverseGaussianDist (double alpha, double beta, double mu, double delta)
 Constructor for a normal inverse gaussian distribution with parameters \(\alpha\) = alpha, \(\beta\) = beta, \(\mu\) = mu and \(\delta\) = delta.
 
double density (double x)
 
double cdf (double x)
 Returns the distribution function \(F(x)\). More...
 
double barF (double x)
 Returns \(\bar{F}(x) = 1 - F(x)\). More...
 
double getMean ()
 Returns the mean of the distribution function.
 
double getVariance ()
 Returns the variance of the distribution function.
 
double getStandardDeviation ()
 Returns the standard deviation of the distribution function.
 
double getAlpha ()
 Returns the parameter \(\alpha\) of this object.
 
double getBeta ()
 Returns the parameter \(\beta\) of this object.
 
double getMu ()
 Returns the parameter \(\mu\) of this object.
 
double getDelta ()
 Returns the parameter \(\delta\) of this object.
 
void setParams (double alpha, double beta, double mu, double delta)
 Sets the parameters \(\alpha\), \(\beta\), \(\mu\) and \(\delta\) of this object.
 
double [] getParams ()
 Returns a table containing the parameters of the current distribution. More...
 
String toString ()
 Returns a String containing information about the current distribution.
 
- Public Member Functions inherited from ContinuousDistribution
abstract double density (double x)
 Returns \(f(x)\), the density evaluated at \(x\). More...
 
double barF (double x)
 Returns the complementary distribution function. More...
 
double inverseBrent (double a, double b, double u, double tol)
 Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method. More...
 
double inverseBisection (double u)
 Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection. More...
 
double inverseF (double u)
 Returns the inverse distribution function \(x = F^{-1}(u)\). More...
 
double getMean ()
 Returns the mean. More...
 
double getVariance ()
 Returns the variance. More...
 
double getStandardDeviation ()
 Returns the standard deviation. More...
 
double getXinf ()
 Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 
double getXsup ()
 Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 
void setXinf (double xa)
 Sets the value \(x_a=\) xa, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 
void setXsup (double xb)
 Sets the value \(x_b=\) xb, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 

Static Public Member Functions

static double density (double alpha, double beta, double mu, double delta, double x)
 Computes the density function ( fNormalInverseGaussian ) for the normal inverse gaussian distribution with parameters \(\alpha\), \(\beta\), \(\mu\) and \(\delta\), evaluated at \(x\).
 
static double cdf (double alpha, double beta, double mu, double delta, double x)
 NOT IMPLEMENTED. More...
 
static double barF (double alpha, double beta, double mu, double delta, double x)
 NOT IMPLEMENTED. More...
 
static double inverseF (double alpha, double beta, double mu, double delta, double u)
 NOT IMPLEMENTED. More...
 
static double [] getMLE (double[] x, int n)
 NOT IMPLEMENTED. More...
 
static NormalInverseGaussianDist getInstanceFromMLE (double[] x, int n)
 NOT IMPLEMENTED. More...
 
static double getMean (double alpha, double beta, double mu, double delta)
 Returns the mean \(E[X] = \mu+ \delta\beta/\gamma\) of the normal inverse gaussian distribution with parameters \(\alpha\), \(\beta\), \(\mu\) and \(\delta\). More...
 
static double getVariance (double alpha, double beta, double mu, double delta)
 Computes and returns the variance \(\mbox{Var}[X] = \delta\alpha^2 / \gamma^3\) of the normal inverse gaussian distribution with parameters \(\alpha\), \(\beta\), \(\mu\) and \(\delta\). More...
 
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 \(\alpha\), \(\beta\), \(\mu\) and \(\delta\). More...
 

Protected Attributes

double alpha
 
double beta
 
double gamma
 
double delta
 
double mu
 
- Protected Attributes inherited from ContinuousDistribution
double supportA = Double.NEGATIVE_INFINITY
 
double supportB = Double.POSITIVE_INFINITY
 

Additional Inherited Members

- Public Attributes inherited from ContinuousDistribution
int decPrec = 15
 
- Static Protected Attributes inherited from ContinuousDistribution
static final double XBIG = 100.0
 
static final double XBIGM = 1000.0
 
static final double [] EPSARRAY
 

Detailed Description

Extends the class ContinuousDistribution for the normal inverse gaussian distribution with location parameter \(\mu\), scale parameter \(\delta> 0\), tail heavyness \(\alpha> 0\), and asymmetry parameter \(\beta\) such that \(0 \le|\beta| < \alpha\).

Its density is

\[ f(x) = \frac{\alpha\delta e^{\delta\gamma+ \beta(x - \mu)} K_1\left(\alpha\sqrt{\delta^2 + (x - \mu)^2}\right)}{\pi\sqrt{\delta^2 + (x - \mu)^2}}, \qquad\mbox{for } -\infty< x < \infty, \tag{fNormalInverseGaussian} \]

where \(K_1\) is the modified Bessel function of the second kind of order 1, and \(\gamma= \sqrt{\alpha^2 - \beta^2}\).

The distribution function is given by

\[ F(x) = \int_{-\infty}^x dt f(t), \tag{FNormalInverseGaussian} \]

Member Function Documentation

◆ barF() [1/2]

double barF ( double  x)

Returns \(\bar{F}(x) = 1 - F(x)\).

Parameters
xvalue at which the complementary distribution function is evaluated
Returns
complementary distribution function evaluated at x

Implements Distribution.

◆ barF() [2/2]

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

NOT IMPLEMENTED.

Computes the complementary distribution function of the normal inverse gaussian distribution with parameters \(\alpha\), \(\beta\), \(\mu\) and \(\delta\), evaluated at \(x\).

◆ cdf() [1/2]

double cdf ( double  x)

Returns the distribution function \(F(x)\).

Parameters
xvalue at which the distribution function is evaluated
Returns
distribution function evaluated at x

Implements Distribution.

◆ cdf() [2/2]

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

NOT IMPLEMENTED.

Computes the distribution function ( FNormalInverseGaussian ) of the normal inverse gaussian distribution with parameters \(\alpha\), \(\beta\), \(\mu\) and \(\delta\), evaluated at \(x\).

◆ getInstanceFromMLE()

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

NOT IMPLEMENTED.

Parameters
xthe list of observations to use to evaluate parameters
nthe number of observations to use to evaluate parameters

◆ getMean()

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

Returns the mean \(E[X] = \mu+ \delta\beta/\gamma\) of the normal inverse gaussian distribution with parameters \(\alpha\), \(\beta\), \(\mu\) and \(\delta\).

Returns
the mean of the normal inverse gaussian distribution \(E[X] = \mu+ \delta\beta/\gamma\)

◆ getMLE()

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

NOT IMPLEMENTED.

Parameters
xthe list of observations used to evaluate parameters
nthe number of observations used to evaluate parameters
Returns
returns the parameters [ \(\hat{\alpha}\), \(\hat{\beta}\), \(\hat{\mu}\), \(\hat{\delta}\)]

◆ getParams()

double [] getParams ( )

Returns a table containing the parameters of the current distribution.

This table is put in regular order: [ \(\alpha\), \(\beta\), \(\mu\), \(\delta\)].

Implements Distribution.

◆ getStandardDeviation()

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

Computes and returns the standard deviation of the normal inverse gaussian distribution with parameters \(\alpha\), \(\beta\), \(\mu\) and \(\delta\).

Returns
the standard deviation of the normal inverse gaussian distribution

◆ getVariance()

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

Computes and returns the variance \(\mbox{Var}[X] = \delta\alpha^2 / \gamma^3\) of the normal inverse gaussian distribution with parameters \(\alpha\), \(\beta\), \(\mu\) and \(\delta\).

Returns
the variance of the normal inverse gaussian distribution \(\mbox{Var}[X] = \delta\alpha^2 / \gamma^3\)

◆ inverseF()

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

NOT IMPLEMENTED.

Computes the inverse of the normal inverse gaussian distribution with parameters \(\alpha\), \(\beta\), \(\mu\) and \(\delta\).


The documentation for this class was generated from the following file: