# bvdist-t2d: Bivariate Student-t Distribution In fMultivar: Rmetrics - Analysing and Modeling Multivariate Financial Return Distributions

## Description

Density, distribution function, and random generation for the bivariate Student-t distribution.

## Usage

 ```1 2 3``` ```dt2d(x, y, rho = 0, nu = 4) pt2d(x, y, rho = 0, nu = 4) rt2d(n, rho = 0, nu = 4) ```

## Arguments

 `n` the number of random deviates to be generated, an integer value. `nu` the number of degrees of freedom, a numeric value ranging between two and infinity, by default four. `rho` the correlation parameter, a numeric value ranging between minus one and one, by default zero. `x, y` two numeric vectors defining the x and y coordinates.

## Value

`pt2d`
returns a two column matrix of probabilities for the bivariate Student-t distribution function.

`dt2d`
returns a two column matrix of densities for the bivariate Student-t distribution function.

`rt2d`
returns a two column matrix of random deviates generated from the bivariate Student-t distribution function.

## Author(s)

Adelchi Azzalini for the underlying `pnorm2d` function,
Diethelm Wuertz for the Rmetrics R-port.

## References

Azzalini A., (2004); The sn Package; R Reference Guide available from www.r-project.org.

Venables W.N., Ripley B.D., (2002); Modern Applied Statistics with S, Fourth Edition, Springer.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```## dt2d - # Bivariate Student-t Density: x <- (-40:40)/10 X <- grid2d(x) z <- dt2d(X\$x, X\$y, rho = 0.5, nu = 6) Z <- list(x = x, y = x, z = matrix(z, ncol = length(x))) # Perspective Plot: persp(Z, theta = -40, phi = 30, col = "steelblue") # Contour Plot: contour(Z) ## pt2d - # Bivariate Student-t Probability: x <- (-40:40)/10 X <- grid2d(x) z <- pt2d(X\$x, X\$y, rho = 0.5, nu = 6) Z <- list(x = x, y = x, z = matrix(z, ncol = length(x))) # Image Plot with Contours: image(Z) contour(Z, add=TRUE) ```

fMultivar documentation built on Nov. 17, 2017, 2:19 p.m.