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:
Collaboration diagram for BiNormalDonnellyDist:
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 |
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:
- BiNormalDonnellyDist.java
