umontreal.ssj.probdistmulti.BiNormalGenzDist Class Reference

Extends the class BiNormalDist for the bivariate normal distribution [94]  (page 84) using Genz’s algorithm as described in [65] . More...

Inheritance diagram for umontreal.ssj.probdistmulti.BiNormalGenzDist:

Public Member Functions
	BiNormalGenzDist (double rho)
	Constructs a BiNormalGenzDist object with default parameters.
	BiNormalGenzDist (double mu1, double sigma1, double mu2, double sigma2, double rho)
	Constructs a BiNormalGenzDist object with parameters \(\mu_1\) = mu1, \(\mu_2\) = mu2, \(\sigma_1\) = sigma1,.
double	cdf (double x, double y)
	Computes the distribution function \(F(x, y)\):
double	barF (double x, double y)
	Computes the upper cumulative distribution function.
Public Member Functions inherited from umontreal.ssj.probdistmulti.BiNormalDist
	BiNormalDist (double rho)
	Constructs a BiNormalDist object with default parameters \(\mu_1 = \mu_2 = 0\), \(\sigma_1 = \sigma_2 = 1\) and correlation.
	BiNormalDist (double mu1, double sigma1, double mu2, double sigma2, double rho)
	Constructs a BiNormalDist object with parameters \(\mu_1\) = mu1, \(\mu_2\) = mu2, \(\sigma_1\) = sigma1,.
double	density (double x, double y)
	Returns \(f(x, y)\), the density of \((X, Y)\) evaluated at \((x, y)\).
double[]	getMean ()
	Returns the mean vector of the distribution, defined as \(\mu_i = E[X_i]\).
double[][]	getCovariance ()
	Returns the variance-covariance matrix of the distribution, defined as \(\sigma_{ij} = E[(X_i - \mu_i)(X_j - \mu_j)]\).
double[][]	getCorrelation ()
	Returns the correlation matrix of the distribution, defined as.
double	getMu1 ()
	Returns the parameter \(\mu_1\).
double	getMu2 ()
	Returns the parameter \(\mu_2\).
double	getSigma1 ()
	Returns the parameter \(\sigma_1\).
double	getSigma2 ()
	Returns the parameter \(\sigma_2\).
Public Member Functions inherited from umontreal.ssj.probdistmulti.ContinuousDistribution2Dim
double	density (double[] x)
	Simply calls density (x[0], x[1]).
double	cdf (double a1, double a2, double b1, double b2)
	Computes the cumulative probability in the square region.
Public Member Functions inherited from umontreal.ssj.probdistmulti.ContinuousDistributionMulti
int	getDimension ()
	Returns the dimension \(d\) of the distribution.

Static Public Member Functions
static double	cdf (double x, double y, double rho)
	Computes the standard binormal distribution ( cdf2binormal ) with the method described in [65] .
static double	cdf (double mu1, double sigma1, double x, double mu2, double sigma2, double y, double rho)
	Computes the binormal distribution function ( cdf1binormal ) with parameters \(\mu_1\) = mu1, \(\mu_2\) = mu2, \(\sigma_1\) = sigma1, \(\sigma_2\) = sigma2 and.
static double	barF (double mu1, double sigma1, double x, double mu2, double sigma2, double y, double rho)
	Computes the upper binormal distribution function ( cdf3binormal ) with parameters \(\mu_1\) = mu1, \(\mu_2\) = mu2, \(\sigma_1\) = sigma1, \(\sigma_2\) = sigma2 and.
static double	barF (double x, double y, double rho)
	Computes the standard upper binormal distribution with \(\mu_1 = \mu_2 = 0\) and \(\sigma_1 = \sigma_2 = 1\).
Static Public Member Functions inherited from umontreal.ssj.probdistmulti.BiNormalDist
static double	density (double x, double y, double rho)
	Computes the standard binormal density function ( f1binormal ) with \(\mu_1 = \mu_2 = 0\) and \(\sigma_1 = \sigma_2 = 1\).
static double	density (double mu1, double sigma1, double x, double mu2, double sigma2, double y, double rho)
	Computes the binormal density function ( f1binormal ) with parameters \(\mu_1\) = mu1, \(\mu_2\) = mu2, \(\sigma_1\) = sigma1, \(\sigma_2\) = sigma2 and.
static double[]	getMean (double mu1, double sigma1, double mu2, double sigma2, double rho)
	Return the mean vector \(E[X] = (\mu_1, \mu_2)\) of the binormal distribution.
static double[][]	getCovariance (double mu1, double sigma1, double mu2, double sigma2, double rho)
	Return the covariance matrix of the binormal distribution.
static double[][]	getCorrelation (double mu1, double sigma1, double mu2, double sigma2, double rho)
	Return the correlation matrix of the binormal distribution.

Additional Inherited Members
Public Attributes inherited from umontreal.ssj.probdistmulti.ContinuousDistribution2Dim
int	decPrec = 15
	Defines the target number of decimals of accuracy when approximating a distribution function, but there is no guarantee that this target is always attained.
Protected Member Functions inherited from umontreal.ssj.probdistmulti.BiNormalDist
void	setParams (double mu1, double sigma1, double mu2, double sigma2, double rho)
	Sets the parameters \(\mu_1\) = mu1, \(\mu_2\) = mu2,.

Detailed Description

Extends the class BiNormalDist for the bivariate normal distribution [94]  (page 84) using Genz’s algorithm as described in [65] .

Definition at line 23 of file BiNormalGenzDist.java.

Constructor & Destructor Documentation

BiNormalGenzDist() [1/2]

umontreal.ssj.probdistmulti.BiNormalGenzDist.BiNormalGenzDist

(

double

rho

)

Constructs a BiNormalGenzDist object with default parameters.

\(\mu_1 = \mu_2 = 0\), \(\sigma_1 = \sigma_2 = 1\) and correlation \(\rho= \) rho.

Definition at line 57 of file BiNormalGenzDist.java.

BiNormalGenzDist() [2/2]

umontreal.ssj.probdistmulti.BiNormalGenzDist.BiNormalGenzDist	(	double	mu1,
		double	sigma1,
		double	mu2,
		double	sigma2,
		double	rho )

Constructs a BiNormalGenzDist object with parameters \(\mu_1\) = mu1, \(\mu_2\) = mu2, \(\sigma_1\) = sigma1,.

\(\sigma_2\) = sigma2 and \(\rho\) = rho.

Definition at line 67 of file BiNormalGenzDist.java.

Member Function Documentation

barF() [1/3]

double umontreal.ssj.probdistmulti.BiNormalGenzDist.barF ( double mu1, double sigma1, double x, double mu2, double sigma2, double y, double rho )

static

Computes the upper binormal distribution function ( cdf3binormal ) with parameters \(\mu_1\) = mu1, \(\mu_2\) = mu2, \(\sigma_1\) = sigma1, \(\sigma_2\) = sigma2 and.

\(\rho\) = rho. Uses the fast Drezner-Wesolowsky method described in [53] . The absolute error is expected to be smaller than \(2 \cdot10^{-7}\).

Reimplemented from umontreal.ssj.probdistmulti.BiNormalDist.

Definition at line 240 of file BiNormalGenzDist.java.

barF() [2/3]

double umontreal.ssj.probdistmulti.BiNormalGenzDist.barF	(	double	x,
		double	y )

Computes the upper cumulative distribution function.

\(\overline{F}(x, y)\):

\[ \overline{F}(x, y) = P[X\ge x, Y \ge y] = \int^{\infty}_x ds \int^{\infty}_y dt  f(s, t). \]

Parameters

x	value \(x\) at which the upper distribution is evaluated
y	value \(y\) at which the upper distribution is evaluated

Returns

upper distribution function evaluated at \((x, y)\)

Reimplemented from umontreal.ssj.probdistmulti.BiNormalDist.

Definition at line 236 of file BiNormalGenzDist.java.

barF() [3/3]

double umontreal.ssj.probdistmulti.BiNormalGenzDist.barF ( double x, double y, double rho )

static

Computes the standard upper binormal distribution with \(\mu_1 = \mu_2 = 0\) and \(\sigma_1 = \sigma_2 = 1\).

Uses the fast Drezner-Wesolowsky method described in [53] . The absolute error is expected to be smaller than \(2 \cdot10^{-7}\).

Reimplemented from umontreal.ssj.probdistmulti.BiNormalDist.

Definition at line 250 of file BiNormalGenzDist.java.

cdf() [1/3]

double umontreal.ssj.probdistmulti.BiNormalGenzDist.cdf ( double mu1, double sigma1, double x, double mu2, double sigma2, double y, double rho )

static

Computes the binormal distribution function ( cdf1binormal ) with parameters \(\mu_1\) = mu1, \(\mu_2\) = mu2, \(\sigma_1\) = sigma1, \(\sigma_2\) = sigma2 and.

\(\rho\) = rho. Uses the fast Drezner-Wesolowsky method described in [53] . The absolute error is expected to be smaller than \(2 \cdot10^{-7}\).

Reimplemented from umontreal.ssj.probdistmulti.BiNormalDist.

Definition at line 222 of file BiNormalGenzDist.java.

cdf() [2/3]

double umontreal.ssj.probdistmulti.BiNormalGenzDist.cdf	(	double	x,
		double	y )

Computes the distribution function \(F(x, y)\):

\[ F(x, y) = P[X\le x, Y \le y] = \int_{-\infty}^x ds \int_{-\infty}^y dt  f(s, t). \]

Parameters

x	value \(x\) at which the distribution function is evaluated
y	value \(y\) at which the distribution function is evaluated

Returns

distribution function evaluated at \((x, y)\)

Reimplemented from umontreal.ssj.probdistmulti.BiNormalDist.

Definition at line 232 of file BiNormalGenzDist.java.

cdf() [3/3]

double umontreal.ssj.probdistmulti.BiNormalGenzDist.cdf ( double x, double y, double rho )

static

Computes the standard binormal distribution ( cdf2binormal ) with the method described in [65] .

The code for the cdf was translated directly from the Matlab code written by Alan Genz and available from his web page at http://www.math.wsu.edu/faculty/genz/homepage (the code is copyrighted by Alan Genz and is included in this package with the kind permission of the author). The absolute error is expected to be smaller than \(0.5 \cdot10^{-15}\).

Reimplemented from umontreal.ssj.probdistmulti.BiNormalDist.

Definition at line 82 of file BiNormalGenzDist.java.

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

• src/main/java/umontreal/ssj/probdistmulti/BiNormalGenzDist.java