fCopulae (version 3000.79)

elliptical2d: Bivariate Elliptical Densities

Description

Density function for bivariate elliptical distributions.

Usage

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

Arguments

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 a

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

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".

x, y

two numeric vectors defining the x and y coordinates.

Value

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

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

## 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)))
   persp(Z, theta = -40, phi = 30, col = "steelblue")