Extends the class BiNormalDist for the bivariate normal distribution [94] (page 84) using a translation of Donnelly’s Fortran code in [52] . More...

Inheritance diagram for umontreal.ssj.probdistmulti.BiNormalDonnellyDist:

Public Member Functions
	BiNormalDonnellyDist (double rho, int ndig)
	Constructor with default parameters \(\mu_1 = \mu_2 = 0\),.
	BiNormalDonnellyDist (double rho)
	Same as `BiNormalDonnellyDist(rho, 15)`.
	BiNormalDonnellyDist (double mu1, double sigma1, double mu2, double sigma2, double rho, int ndig)
	Constructor with parameters \(\mu_1\) = mu1, \(\mu_2\) = mu2, \(\sigma_1\) = sigma1, \(\sigma_2\) = sigma2,.
	BiNormalDonnellyDist (double mu1, double sigma1, double mu2, double sigma2, double rho)
	Same as `BiNormalDonnellyDist(mu1, sigma1, mu2, sigma2, rho, 15)`.
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, int ndig)
	The following methods use the parameter ndig for the number of digits of absolute accuracy.
static double	cdf (double mu1, double sigma1, double x, double mu2, double sigma2, double y, double rho, int ndig)
	Computes the binormal distribution function ( `cdf1binormal` ) with parameters \(\mu_1\) = mu1, \(\mu_2\) = mu2, \(\sigma_1\) = sigma1, \(\sigma_2\) = sigma2, correlation \(\rho\) = rho and ndig decimal digits of accuracy.
static double	barF (double mu1, double sigma1, double x, double mu2, double sigma2, double y, double rho, int ndig)
	Computes the upper binormal distribution function ( `cdf3binormal` ) with parameters \(\mu_1\) = mu1, \(\mu_2\) = mu2, \(\sigma_1\) = sigma1, \(\sigma_2\) = sigma2,.
static double	barF (double x, double y, double rho, int ndig)
	Computes the upper standard binormal distribution function ( `cdf3binormal` ) with parameters \(\rho\) = rho and ndig decimal digits of accuracy.
static double	cdf (double x, double y, double rho)
	Computes the standard binormal distribution ( `cdf2binormal` ) using the fast Drezner-Wesolowsky method described in.
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 a translation of Donnelly’s Fortran code in [52] .

Definition at line 24 of file BiNormalDonnellyDist.java.

Constructor & Destructor Documentation

◆ BiNormalDonnellyDist() [1/4]

umontreal.ssj.probdistmulti.BiNormalDonnellyDist.BiNormalDonnellyDist	(	double	rho,
		int	ndig )

Constructor with default parameters \(\mu_1 = \mu_2 = 0\),.

\(\sigma_1 = \sigma_2 = 1\), correlation \(\rho= \) rho , and \(d = \) ndig digits of accuracy (the absolute error is smaller than \(10^{-d}\)). Restriction: \(d \le15\).

Definition at line 63 of file BiNormalDonnellyDist.java.

◆ BiNormalDonnellyDist() [2/4]

umontreal.ssj.probdistmulti.BiNormalDonnellyDist.BiNormalDonnellyDist ( double rho )

Same as BiNormalDonnellyDist(rho, 15).

Definition at line 74 of file BiNormalDonnellyDist.java.

◆ BiNormalDonnellyDist() [3/4]

umontreal.ssj.probdistmulti.BiNormalDonnellyDist.BiNormalDonnellyDist	(	double	mu1,
		double	sigma1,
		double	mu2,
		double	sigma2,
		double	rho,
		int	ndig )

Constructor with parameters \(\mu_1\) = mu1, \(\mu_2\) = mu2, \(\sigma_1\) = sigma1, \(\sigma_2\) = sigma2,.

\(\rho\) = rho, and \(d = \) ndig digits of accuracy. Restriction: \(d \le15\).

Definition at line 85 of file BiNormalDonnellyDist.java.

◆ BiNormalDonnellyDist() [4/4]

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

Same as BiNormalDonnellyDist(mu1, sigma1, mu2, sigma2, rho, 15).

Definition at line 96 of file BiNormalDonnellyDist.java.

Member Function Documentation

◆ barF() [1/5]

double umontreal.ssj.probdistmulti.BiNormalDonnellyDist.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 311 of file BiNormalDonnellyDist.java.

◆ barF() [2/5]

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

static

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

\(\rho\) = rho and ndig decimal digits of accuracy.

Definition at line 275 of file BiNormalDonnellyDist.java.

◆ barF() [3/5]

double umontreal.ssj.probdistmulti.BiNormalDonnellyDist.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 307 of file BiNormalDonnellyDist.java.

◆ barF() [4/5]

double umontreal.ssj.probdistmulti.BiNormalDonnellyDist.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 315 of file BiNormalDonnellyDist.java.

◆ barF() [5/5]

double umontreal.ssj.probdistmulti.BiNormalDonnellyDist.barF	(	double	x,
		double	y,
		double	rho,
		int	ndig )

static

Computes the upper standard binormal distribution function ( cdf3binormal ) with parameters \(\rho\) = rho and ndig decimal digits of accuracy.

Definition at line 291 of file BiNormalDonnellyDist.java.

◆ cdf() [1/5]

double umontreal.ssj.probdistmulti.BiNormalDonnellyDist.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 303 of file BiNormalDonnellyDist.java.

◆ cdf() [2/5]

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

static

Computes the binormal distribution function ( cdf1binormal ) with parameters \(\mu_1\) = mu1, \(\mu_2\) = mu2, \(\sigma_1\) = sigma1, \(\sigma_2\) = sigma2, correlation \(\rho\) = rho and ndig decimal digits of accuracy.

Definition at line 256 of file BiNormalDonnellyDist.java.

◆ cdf() [3/5]

double umontreal.ssj.probdistmulti.BiNormalDonnellyDist.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 295 of file BiNormalDonnellyDist.java.

◆ cdf() [4/5]

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

static

Computes the standard binormal distribution ( cdf2binormal ) using 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 299 of file BiNormalDonnellyDist.java.

◆ cdf() [5/5]

double umontreal.ssj.probdistmulti.BiNormalDonnellyDist.cdf	(	double	x,
		double	y,
		double	rho,
		int	ndig )

static

The following methods use the parameter ndig for the number of digits of absolute accuracy.

If the same methods are called without the ndig parameter, a default value of ndig = 15 will be used.

Computes the standard binormal distribution ( cdf2binormal ) with the method described in [52] , where ndig is the number of decimal digits of accuracy provided (ndig \(\le15\)). The code was translated from the Fortran program written by T. G. Donnelly and copyrighted by the ACM (see http://www.acm.org/pubs/copyright_policy/#Notice). The absolute error is expected to be smaller than \(10^{-d}\), where \(d=\) ndig.

Definition at line 115 of file BiNormalDonnellyDist.java.

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

src/main/java/umontreal/ssj/probdistmulti/BiNormalDonnellyDist.java

SSJ API Documentation Stochastic Simulation in Java

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ BiNormalDonnellyDist() [1/4]

◆ BiNormalDonnellyDist() [2/4]

◆ BiNormalDonnellyDist() [3/4]

◆ BiNormalDonnellyDist() [4/4]

Member Function Documentation

◆ barF() [1/5]

◆ barF() [2/5]

◆ barF() [3/5]

◆ barF() [4/5]

◆ barF() [5/5]

◆ cdf() [1/5]

◆ cdf() [2/5]

◆ cdf() [3/5]

◆ cdf() [4/5]

◆ cdf() [5/5]