Extends the class ContinuousDistribution for the normal inverse gaussian distribution with location parameter \(\mu\), scale parameter. More...

Inheritance diagram for umontreal.ssj.probdist.NormalInverseGaussianDist:

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,.
double	density (double x)
	Returns \(f(x)\), the density evaluated at \(x\).
double	cdf (double x)
	Returns the distribution function \(F(x)\).
double	barF (double x)
	Returns the complementary distribution function.
double	getMean ()
	Returns the mean.
double	getVariance ()
	Returns the variance.
double	getStandardDeviation ()
	Returns the standard deviation.
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.
double[]	getParams ()
	Returns a table containing the parameters of the current distribution.
String	toString ()
	Returns a String containing information about the current distribution.
Public Member Functions inherited from umontreal.ssj.probdist.ContinuousDistribution
double	inverseBrent (double a, double b, double u, double tol)
	Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method.
double	inverseBisection (double u)
	Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection.
double	inverseF (double u)
	Returns the inverse distribution function \(x = F^{-1}(u)\).
double	getXinf ()
	Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
double	getXsup ()
	Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
void	setXinf (double xa)
	Sets the value \(x_a=\) xa, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
void	setXsup (double xb)
	Sets the value \(x_b=\) xb, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).

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.
static double	barF (double alpha, double beta, double mu, double delta, double x)
	NOT IMPLEMENTED.
static double	inverseF (double alpha, double beta, double mu, double delta, double u)
	NOT IMPLEMENTED.
static double[]	getMLE (double[] x, int n)
	NOT IMPLEMENTED.
static NormalInverseGaussianDist	getInstanceFromMLE (double[] x, int n)
	NOT IMPLEMENTED.
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.
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 \(\delta\).
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 \(\alpha\), \(\beta\),.

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

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

Definition at line 51 of file NormalInverseGaussianDist.java.

Constructor & Destructor Documentation

◆ NormalInverseGaussianDist()

umontreal.ssj.probdist.NormalInverseGaussianDist.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.

Definition at line 64 of file NormalInverseGaussianDist.java.

Member Function Documentation

◆ barF() [1/2]

double umontreal.ssj.probdist.NormalInverseGaussianDist.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 \(x\).

Definition at line 152 of file NormalInverseGaussianDist.java.

◆ barF() [2/2]

double umontreal.ssj.probdist.NormalInverseGaussianDist.barF ( double x )

Returns the complementary distribution function.

The default implementation computes \(\bar{F}(x) = 1 - F(x)\).

Parameters

x	value at which the complementary distribution function is evaluated

Returns: complementary distribution function evaluated at x

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 76 of file NormalInverseGaussianDist.java.

◆ cdf() [1/2]

double umontreal.ssj.probdist.NormalInverseGaussianDist.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 \(x\).

Definition at line 127 of file NormalInverseGaussianDist.java.

◆ cdf() [2/2]

double umontreal.ssj.probdist.NormalInverseGaussianDist.cdf ( double x )

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

Parameters

x	value at which the distribution function is evaluated

Returns: distribution function evaluated at x

Implements umontreal.ssj.probdist.Distribution.

Definition at line 72 of file NormalInverseGaussianDist.java.

◆ density() [1/2]

double umontreal.ssj.probdist.NormalInverseGaussianDist.density	(	double	alpha,
		double	beta,
		double	mu,
		double	delta,
		double	x )

static

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

Definition at line 99 of file NormalInverseGaussianDist.java.

◆ density() [2/2]

double umontreal.ssj.probdist.NormalInverseGaussianDist.density ( double x )

Returns \(f(x)\), the density evaluated at \(x\).

Parameters

x	value at which the density is evaluated

Returns: density function evaluated at x

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 68 of file NormalInverseGaussianDist.java.

◆ getAlpha()

double umontreal.ssj.probdist.NormalInverseGaussianDist.getAlpha ( )

Returns the parameter \(\alpha\) of this object.

Definition at line 251 of file NormalInverseGaussianDist.java.

◆ getBeta()

double umontreal.ssj.probdist.NormalInverseGaussianDist.getBeta ( )

Returns the parameter \(\beta\) of this object.

Definition at line 258 of file NormalInverseGaussianDist.java.

◆ getDelta()

double umontreal.ssj.probdist.NormalInverseGaussianDist.getDelta ( )

Returns the parameter \(\delta\) of this object.

Definition at line 272 of file NormalInverseGaussianDist.java.

◆ getInstanceFromMLE()

NormalInverseGaussianDist umontreal.ssj.probdist.NormalInverseGaussianDist.getInstanceFromMLE	(	double[]	x,
		int	n )

static

NOT IMPLEMENTED.

Parameters

x	the list of observations to use to evaluate parameters
n	the number of observations to use to evaluate parameters

Definition at line 192 of file NormalInverseGaussianDist.java.

◆ getMean() [1/2]

double umontreal.ssj.probdist.NormalInverseGaussianDist.getMean ( )

Returns the mean.

Returns: the mean

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 80 of file NormalInverseGaussianDist.java.

◆ getMean() [2/2]

double umontreal.ssj.probdist.NormalInverseGaussianDist.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 \(E[X] = \mu+ \delta\beta/\gamma\)

Definition at line 205 of file NormalInverseGaussianDist.java.

◆ getMLE()

double[] umontreal.ssj.probdist.NormalInverseGaussianDist.getMLE	(	double[]	x,
		int	n )

static

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 [ \(\hat{\alpha}\), \(\hat{\beta}\), \(\hat{\mu}\), \(\hat{\delta}\)]

Definition at line 174 of file NormalInverseGaussianDist.java.

◆ getMu()

double umontreal.ssj.probdist.NormalInverseGaussianDist.getMu ( )

Returns the parameter \(\mu\) of this object.

Definition at line 265 of file NormalInverseGaussianDist.java.

◆ getParams()

double[] umontreal.ssj.probdist.NormalInverseGaussianDist.getParams ( )

Returns a table containing the parameters of the current distribution.

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

Implements umontreal.ssj.probdist.Distribution.

Definition at line 302 of file NormalInverseGaussianDist.java.

◆ getStandardDeviation() [1/2]

double umontreal.ssj.probdist.NormalInverseGaussianDist.getStandardDeviation ( )

Returns the standard deviation.

Returns: the standard deviation

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 88 of file NormalInverseGaussianDist.java.

◆ getStandardDeviation() [2/2]

double umontreal.ssj.probdist.NormalInverseGaussianDist.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

Definition at line 244 of file NormalInverseGaussianDist.java.

◆ getVariance() [1/2]

double umontreal.ssj.probdist.NormalInverseGaussianDist.getVariance ( )

Returns the variance.

Returns: the variance

Reimplemented from umontreal.ssj.probdist.ContinuousDistribution.

Definition at line 84 of file NormalInverseGaussianDist.java.

◆ getVariance() [2/2]

double umontreal.ssj.probdist.NormalInverseGaussianDist.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 \(\mbox{Var}[X] = \delta\alpha^2 / \gamma^3\)

Definition at line 225 of file NormalInverseGaussianDist.java.

◆ inverseF()

double umontreal.ssj.probdist.NormalInverseGaussianDist.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 \(\delta\).

Definition at line 162 of file NormalInverseGaussianDist.java.

◆ setParams()

void umontreal.ssj.probdist.NormalInverseGaussianDist.setParams	(	double	alpha,
		double	beta,
		double	mu,
		double	delta )

Sets the parameters \(\alpha\), \(\beta\), \(\mu\) and.

\(\delta\) of this object.

Definition at line 281 of file NormalInverseGaussianDist.java.

◆ toString()

String umontreal.ssj.probdist.NormalInverseGaussianDist.toString ( )

Returns a String containing information about the current distribution.

Definition at line 310 of file NormalInverseGaussianDist.java.

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

src/main/java/umontreal/ssj/probdist/NormalInverseGaussianDist.java

SSJ API Documentation Stochastic Simulation in Java

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ NormalInverseGaussianDist()

Member Function Documentation

◆ barF() [1/2]

◆ barF() [2/2]

◆ cdf() [1/2]

◆ cdf() [2/2]

◆ density() [1/2]

◆ density() [2/2]

◆ getAlpha()

◆ getBeta()

◆ getDelta()

◆ getInstanceFromMLE()

◆ getMean() [1/2]

◆ getMean() [2/2]

◆ getMLE()

◆ getMu()

◆ getParams()

◆ getStandardDeviation() [1/2]

◆ getStandardDeviation() [2/2]

◆ getVariance() [1/2]

◆ getVariance() [2/2]

◆ inverseF()

◆ setParams()

◆ toString()