Extends the class ContinuousDistribution2Dim for the standard bivariate Student’s \(t\) distribution [98] (page 132). More...
Public Member Functions | |
| BiStudentDist (int nu, double rho) | |
Constructs a BiStudentDist object with correlation \(\rho= \) rho and \(\nu\) = nu degrees of freedom. | |
| double | density (double x, double y) |
| double | cdf (double x, double y) |
| double | barF (double x, double y) |
| double [] | getMean () |
| double [][] | getCovariance () |
| double [][] | getCorrelation () |
 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 | density (int nu, double x, double y, double rho) |
Computes the standard bivariate Student’s \(t\) density function ( pdf1bit ) with correlation \(\rho\) = rho and \(\nu\) = nu degrees of freedom. | |
| static double | cdf (int nu, double x, double y, double rho) |
| Computes the standard bivariate Student’s \(t\) distribution ( cdf1bit ) using the method described in [67] . More... | |
| static double | barF (int nu, double x, double y, double rho) |
| Computes the standard upper bivariate Student’s \(t\) distribution ( cdf2bit ). | |
| static double [] | getMean (int nu, double rho) |
| Returns the mean vector \(E[X] = (0, 0)\) of the bivariate Student’s \(t\) distribution. | |
| static double [][] | getCovariance (int nu, double rho) |
| Returns the covariance matrix of the bivariate Student’s \(t\) distribution. | |
| static double [][] | getCorrelation (int nu, double rho) |
| Returns the correlation matrix of the bivariate Student’s \(t\) distribution. | |
Protected Member Functions | |
| void | setParams (int nu, double rho) |
Sets the parameters \(\nu\) = nu and \(\rho\) = rho of this object. | |
Protected Attributes | |
| int | nu |
| double | rho |
| double | facRho |
| Protected Attributes inherited from ContinuousDistributionMulti | |
| int | dimension |
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. | |
| Static Protected Attributes inherited from ContinuousDistribution2Dim | |
| static final double | XINF = Double.MAX_VALUE |
| static final double | XBIG = 1000.0 |
| static final double [] | EPSARRAY |
Detailed Description
Extends the class ContinuousDistribution2Dim for the standard bivariate Student’s \(t\) distribution [98] (page 132).
The correlation between \(X\) and \(Y\) is \(\rho\) and the number of degrees of freedom is \(\nu\). Its probability density is
\[ f (x, y) = \frac{1}{2\pi\sqrt{1-\rho^2}}\left[1 + \frac{x^2 - 2\rho x y + y^2}{\nu(1-\rho^2)}\right]^{-(\nu+ 2)/2} , \tag{pdf1bit} \]
and the corresponding distribution function (the cdf) is
\[ T_{\nu}(x, y, \rho) = \frac{1}{2\pi\sqrt{1-\rho^2}} \int_{-\infty}^x dx \int_{-\infty}^y dy f (x, y). \tag{cdf1bit} \]
We also define the upper distribution function called barF as
\[ \overline{T}_{\nu}(x, y, \rho) = \frac{1}{2\pi\sqrt{1-\rho^2}} \int^{\infty}_x dx \int^{\infty}_y dy f(x,y). \tag{cdf2bit} \]
Member Function Documentation
◆ cdf()
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static |
Computes the standard bivariate Student’s \(t\) distribution ( cdf1bit ) using 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 correlation is \(\rho= \) rho and the number of degrees of freedom is \(\nu\) = nu.
The documentation for this class was generated from the following file:
- BiStudentDist.java
