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

Extends the class BiNormalDist for the bivariate normal distribution [98]  (page 84) using a translation of Donnelly’s Fortran code in [53] . More...

Inheritance diagram for BiNormalDonnellyDist:
[legend]
Collaboration diagram for BiNormalDonnellyDist:
[legend]

Public Member Functions

 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 \(10^{-d}\)). More...
 
 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, \(\rho\) = rho, and \(d = \) ndig digits of accuracy. More...
 
 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)
 
double barF (double x, double y)
 
- Public Member Functions inherited from BiNormalDist
 BiNormalDist (double rho)
 Constructs a BiNormalDist object with default parameters \(\mu_1 = \mu_2 = 0\), \(\sigma_1 = \sigma_2 = 1\) and correlation \(\rho= \) rho.
 
 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, \(\sigma_2\) = sigma2 and \(\rho\) = rho.
 
double density (double x, double y)
 
double cdf (double x, double y)
 
double barF (double x, double y)
 
double [] getMean ()
 
double [][] getCovariance ()
 
double [][] getCorrelation ()
 
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 ContinuousDistribution2Dim
abstract double density (double x, double y)
 Returns \(f(x, y)\), the density of \((X, Y)\) evaluated at \((x, y)\). More...
 
double density (double[] x)
 Simply calls density (x[0], x[1]). More...
 
abstract double cdf (double x, double y)
 Computes the distribution function \(F(x, y)\):

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

. More...

 
double barF (double x, double y)
 Computes the upper cumulative distribution function \(\overline{F}(x, y)\):

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

. More...

 
double cdf (double a1, double a2, double b1, double b2)
 Computes the cumulative probability in the square region

\[ P[a_1 \le X \le b_1,\: a_2 \le Y \le b_2] = \int_{a_1}^{b_1} dx \int_{a_2}^{b_2} dy  f(x, y). \]

. More...

 
- Public Member Functions inherited from ContinuousDistributionMulti
abstract double density (double[] x)
 Returns \(f(x_1, x_2, …, x_d)\), the probability density of \(X\) evaluated at the point \(x\), where \(x = \{x_1, x_2, …, x_d\}\). More...
 
int getDimension ()
 Returns the dimension \(d\) of the distribution.
 
abstract double [] getMean ()
 Returns the mean vector of the distribution, defined as \(\mu_i = E[X_i]\).
 
abstract double [][] getCovariance ()
 Returns the variance-covariance matrix of the distribution, defined as
\(\sigma_{ij} = E[(X_i - \mu_i)(X_j - \mu_j)]\).
 
abstract double [][] getCorrelation ()
 Returns the correlation matrix of the distribution, defined as \(\rho_{ij} = \sigma_{ij}/\sqrt{\sigma_{ii}\sigma_{jj}}\).
 

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. More...
 
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, \(\rho\) = rho and ndig decimal digits of accuracy.
 
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)
 
static double cdf (double mu1, double sigma1, double x, double mu2, double sigma2, double y, double rho)
 
static double barF (double mu1, double sigma1, double x, double mu2, double sigma2, double y, double rho)
 
static double barF (double x, double y, double rho)
 
- Static Public Member Functions inherited from 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 \(\rho\) = rho.
 
static double cdf (double x, double y, double rho)
 Computes the standard binormal distribution ( cdf2binormal ) using the fast Drezner-Wesolowsky method described in [54] . More...
 
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 \(\rho\) = rho. More...
 
static double barF (double x, double y, double rho)
 Computes the standard upper binormal distribution with \(\mu_1 = \mu_2 = 0\) and \(\sigma_1 = \sigma_2 = 1\). More...
 
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 \(\rho\) = rho. More...
 
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 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 BiNormalDist
void setParams (double mu1, double sigma1, double mu2, double sigma2, double rho)
 Sets the parameters \(\mu_1\) = mu1, \(\mu_2\) = mu2, \(\sigma_1\) = sigma1, \(\sigma_2\) = sigma2 and \(\rho\) = rho of this object.
 
- Static Protected Member Functions inherited from BiNormalDist
static double Gauss (double z)
 
static double specialCDF (double x, double y, double rho, double xbig)
 
- Protected Attributes inherited from BiNormalDist
int ndigit
 
double mu1
 
double sigma1
 
double rho
 
double racRho
 
double detS
 
- Protected Attributes inherited from ContinuousDistributionMulti
int dimension
 
- Static Protected Attributes inherited from BiNormalDist
static final double RHO_SMALL = 1.0e-8
 
- Static Protected Attributes inherited from ContinuousDistribution2Dim
static final double XINF = Double.MAX_VALUE
 
static final double XBIG = 1000.0
 
static final double [] EPSARRAY
 
- Package Attributes inherited from BiNormalDist
double mu2
 
double sigma2
 

Detailed Description

Extends the class BiNormalDist for the bivariate normal distribution [98]  (page 84) using a translation of Donnelly’s Fortran code in [53] .

Constructor & Destructor Documentation

◆ BiNormalDonnellyDist() [1/2]

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: \(d \le15\).

◆ BiNormalDonnellyDist() [2/2]

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: \(d \le15\).

Member Function Documentation

◆ cdf()

static double 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 [53] , 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.


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