elliptical2d {fMultivar} | R Documentation |
Density function for bivariate elliptical distributions.
delliptical2d(x, y = x, rho = 0, param = NULL, type = c("norm", "cauchy", "t", "logistic", "laplace", "kotz", "epower"), output = c("vector", "list"))
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 $x , y , and z which can be directly
used for example by 2D plotting functions.
|
param |
additional parameters to specify the bivariate density function.
Only effective for the Kotz and Exponential Power distribution.
For the Kotz distribution we can specify a numeric value, by default
defined as param=c(r=sqrt(2)) , and for the Exponential
Power distribution a numeric vector, by default defined as
param=c(r=sqrt(2)),s=1/2 .
|
rho |
the correlation parameter, a numeric value ranging between minus one and one, by default zero. |
type |
the type of the elliptical copula. A character string selected
from: "norm" , "cauchy" , "t" , "laplace" ,
"kotz" , or "epower" .
|
x, y |
two numeric vectors defining the x and y coordinates. |
delliptical2d
returns a two column matrix of densities for the selected bivariate
elliptical distribution function.
Diethelm Wuertz for the Rmetrics R-port.
Azzalini A., (2004); The sn Package; R Reference Guide available from www.r-project.org.
Venables W.N., Ripley B.D., (2002); Modern Applied Statistics with S, Fourth Edition, Springer.
## Kotz' Elliptical Density: x = (-40:40)/10 X = grid2d(x) z = delliptical2d(X$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")