# bvdist-elliptical2d: Bivariate Elliptical Densities In fMultivar: Rmetrics - Analysing and Modeling Multivariate Financial Return Distributions

## Description

Density function for bivariate elliptical distributions.

## Usage

 ```1 2``` ```delliptical2d(x, y, rho = 0, param = NULL, type = c("norm", "cauchy", "t", "logistic", "laplace", "kotz", "epower"), output = c("vector", "list")) ```

## Arguments

 `x, y` two numeric vectors defining the x and y coordinates. `output` output - a character string specifying how the output should be formatted. By default a vector of the same length as `u` and `v`. If specified as `"list"` then `u` and `v` are expected to span a two-dimensional grid as outputted by the function `grid2d` and the function returns a list with elements `\$x`, `y`, and `z` which can be directly used for example by 2D plotting functions. `param` additional parameters to specify the bivariate density function. Only effective for the Kotz and Exponential Power distribution. For the Kotz distribution we can specify a numeric value, by default defined as `param=c(r=sqrt(2))`, and for the Exponential Power distribution a numeric vector, by default defined as `param=c(r=sqrt(2)),s=1/2`. `rho` the correlation parameter, a numeric value ranging between minus one and one, by default zero. `type` the type of the elliptical copula. A character string selected from: `"norm"`, `"cauchy"`, `"t"`, `"laplace"`, `"kotz"`, or `"epower"`.

## Value

`delliptical2d`
returns a two column matrix of densities for the selected bivariate elliptical distribution function.

## Author(s)

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``` ```## delliptical2d - # Kotz' Elliptical Density: x <- (-40:40)/10 X <- grid2d(x) z <- delliptical2d(X\$x, X\$y, rho = 0.5, type = "kotz") Z <- list(x = x, y = x, z = matrix(z, ncol = length(x))) ## Perspective Plot: persp(Z, theta = -40, phi = 30, col = "steelblue") ## Image Plot with Contours: image(Z, main = "Bivariate Kotz") contour(Z, add=TRUE) ## Internal Density Slider: ## Not run: .delliptical2dSlider() ## End(Not run) ```

fMultivar documentation built on March 13, 2020, 3:06 a.m.