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

x	value 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

x	value 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

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

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

Returns: returns the parameters [ \(\hat{\alpha}\), \(\hat{\beta}\), \(\hat{\mu}\), \(\hat{\delta}\)]

◆ 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:

NormalInverseGaussianDist.java

Public Member Functions

Static Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ barF() [1/2]

◆ barF() [2/2]

◆ cdf() [1/2]

◆ cdf() [2/2]

◆ getInstanceFromMLE()

◆ getMean()

◆ getMLE()

◆ getParams()

◆ getStandardDeviation()

◆ getVariance()

◆ inverseF()