Extends the class BiNormalDist for the bivariate normal distribution [98] (page 84) using Genz’s algorithm as described in [67] . More...
Inheritance diagram for BiNormalGenzDist:
Collaboration diagram for BiNormalGenzDist:
Public Member Functions | |
| BiNormalGenzDist (double rho) | |
Constructs a BiNormalGenzDist object with default parameters \(\mu_1 = \mu_2 = 0\), \(\sigma_1 = \sigma_2 = 1\) and correlation \(\rho= \) rho. | |
| 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. | |
| 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) |
| Computes the standard binormal distribution ( cdf2binormal ) with the method described in [67] . More... | |
| 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 Genz’s algorithm as described in [67] .
Member Function Documentation
◆ cdf()
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static |
Computes the standard binormal distribution ( cdf2binormal ) with the method described in [67] .
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 \(0.5 \cdot10^{-15}\).
The documentation for this class was generated from the following file:
- BiNormalGenzDist.java
