BiStudentDist (Java Libraries for Stochastic Simulation)

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

```
public class BiStudentDist
extends 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

T_ν(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) = ∫^∞_xdx∫^∞_ydy f (x, y)/(2π(1 - r^2)^1/2).

Field Summary
- Fields inherited from class umontreal.iro.lecuyer.probdistmulti.ContinuousDistribution2Dim
  decPrec

Constructor Summary

Constructors
Constructor and Description

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

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

Method Summary

Methods
Modifier and Type	Method and Description
`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 ρ_ij = σ_ij/(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 σ_ij = E[(X_i - μ_i)(X_j - μ_j)].
`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 μ_i = E[X_i].
`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] = ∫^∞_xds∫^∞_ydt 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 μ_i = E[X_i].
    
    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
    σ_ij = E[(X_i - μ_i)(X_j - μ_j)].
    
    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 ρ_ij = σ_ij/(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.

Class BiStudentDist

Field Summary

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

Constructor Summary

Method Summary

Methods inherited from class umontreal.iro.lecuyer.probdistmulti.ContinuousDistribution2Dim

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

Methods inherited from class java.lang.Object

Constructor Detail

BiStudentDist

Method Detail

density

cdf

barF

density

cdf

barF

getMean

getMean

getCovariance

getCovariance

getCorrelation

getCorrelation