SSJ
V. 2.6.

## umontreal.iro.lecuyer.probdistmulti Class BiStudentDist

```java.lang.Object
umontreal.iro.lecuyer.probdistmulti.ContinuousDistributionMulti
umontreal.iro.lecuyer.probdistmulti.ContinuousDistribution2Dim
umontreal.iro.lecuyer.probdistmulti.BiStudentDist
```

`public class BiStudentDistextends ContinuousDistribution2Dim`

Extends the class `ContinuousDistribution2Dim` for the standard bivariate Student's t distribution. The correlation between X and Y is r and the number of degrees of freedom is ν. Its probability density is

f (x, y) = (1 + (x2 -2ρxy + y2)/(ν(1 - ρ2)))-(ν+2)/2/(2π(1-r^2)1/2),

and the corresponding distribution function (the cdf) is

Tν(x, y, r) = ∫-∞xdx-∞ydy f (x, y)/(2π(1 - r^2)1/2).

We also define the upper distribution function called barF as

bar(T)ν(x, y, r) = ∫xdxydy f (x, y)/(2π(1 - r^2)1/2).

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdistmulti.ContinuousDistribution2Dim
`decPrec`

Constructor Summary
```BiStudentDist(int nu, double rho)```
Constructs a BiStudentDist object with correlation ρ = rho and ν = nu degrees of freedom.

Method Summary
` double` ```barF(double x, double y)```
.
`static double` ```barF(int nu, double x, double y, double rho)```
Computes the standard upper bivariate Student's t distribution.
` double` ```cdf(double x, double y)```
.
`static double` ```cdf(int nu, double x, double y, double rho)```
Computes the standard bivariate Student's t distribution using the method described in.
` double` ```density(double x, double y)```
Returns f (x, y), the density of (X, Y) evaluated at (x, y).
`static double` ```density(int nu, double x, double y, double rho)```
Computes the standard bivariate Student's t density function with correlation ρ = rho and ν = nu degrees of freedom.
` double[][]` `getCorrelation()`
Returns the correlation matrix of the distribution, defined as ρij = σij/(σ_iiσ_jj)1/2.
`static double[][]` ```getCorrelation(int nu, double rho)```
Returns the correlation matrix of the bivariate Student's t distribution.
` double[][]` `getCovariance()`
Returns the variance-covariance matrix of the distribution, defined as
σij = E[(Xi - μi)(Xj - μj)].
`static double[][]` ```getCovariance(int nu, double rho)```
Returns the covariance matrix of the bivariate Student's t distribution.
` double[]` `getMean()`
Returns the mean vector of the distribution, defined as μi = E[Xi].
`static double[]` ```getMean(int nu, double rho)```
Returns the mean vector E[X] = (0, 0) of the bivariate Student's t distribution.

Methods inherited from class umontreal.iro.lecuyer.probdistmulti.ContinuousDistribution2Dim
`cdf, density`

Methods inherited from class umontreal.iro.lecuyer.probdistmulti.ContinuousDistributionMulti
`getDimension`

Methods inherited from class java.lang.Object
`equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Constructor Detail

### BiStudentDist

```public BiStudentDist(int nu,
double rho)```
Constructs a BiStudentDist object with correlation ρ = rho and ν = nu degrees of freedom.

Method Detail

### density

```public double density(double x,
double y)```
Description copied from class: `ContinuousDistribution2Dim`
Returns f (x, y), the density of (X, Y) evaluated at (x, y).

Specified by:
`density` in class `ContinuousDistribution2Dim`
Parameters:
`x` - value x at which the density is evaluated
`y` - value y at which the density is evaluated
Returns:
density function evaluated at (x, y)

### cdf

```public double cdf(double x,
double y)```
Description copied from class: `ContinuousDistribution2Dim`
. Computes the distribution function F(x, y):

F(x, y) = P[X <= x, Y <= y] = ∫-∞xds-∞ydt f (s, t).

Specified by:
`cdf` in class `ContinuousDistribution2Dim`
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)

### barF

```public double barF(double x,
double y)```
Description copied from class: `ContinuousDistribution2Dim`
. Computes the upper cumulative distribution function bar(F)(x, y):

bar(F)(x, y) = P[X >= x, Y >= y] = ∫xdsydt f (s, t).

Overrides:
`barF` in class `ContinuousDistribution2Dim`
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)

### density

```public static double density(int nu,
double x,
double y,
double rho)```
Computes the standard bivariate Student's t density function with correlation ρ = rho and ν = nu degrees of freedom.

### cdf

```public static double cdf(int nu,
double x,
double y,
double rho)```
Computes the standard bivariate Student's t distribution using the method described in. 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 ρ = rho and the number of degrees of freedom is ν = nu.

### barF

```public static double barF(int nu,
double x,
double y,
double rho)```
Computes the standard upper bivariate Student's t distribution.

### getMean

`public double[] getMean()`
Description copied from class: `ContinuousDistributionMulti`
Returns the mean vector of the distribution, defined as μi = E[Xi].

Specified by:
`getMean` in class `ContinuousDistributionMulti`

### getMean

```public static double[] getMean(int nu,
double rho)```
Returns the mean vector E[X] = (0, 0) of the bivariate Student's t distribution.

### getCovariance

`public double[][] getCovariance()`
Description copied from class: `ContinuousDistributionMulti`
Returns the variance-covariance matrix of the distribution, defined as
σij = E[(Xi - μi)(Xj - μj)].

Specified by:
`getCovariance` in class `ContinuousDistributionMulti`

### getCovariance

```public static double[][] getCovariance(int nu,
double rho)```
Returns the covariance matrix of the bivariate Student's t distribution.

### getCorrelation

`public double[][] getCorrelation()`
Description copied from class: `ContinuousDistributionMulti`
Returns the correlation matrix of the distribution, defined as ρij = σij/(σ_iiσ_jj)1/2.

Specified by:
`getCorrelation` in class `ContinuousDistributionMulti`

### getCorrelation

```public static double[][] getCorrelation(int nu,
double rho)```
Returns the correlation matrix of the bivariate Student's t distribution.

SSJ
V. 2.6.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.