plotmvd: Plot a Bivariate Density

In multvardiv: Multivariate Probability Distributions, Statistical Divergence

Plot a Bivariate Density

Description

Plots the probability density of a multivariate distribution with 2 variables:

• generalized Gaussian distribution (MGGD) with mean vector mu, dispersion matrix Sigma and shape parameter beta

• Cauchy distribution (MCD) with location parameter mu and scatter matrix Sigma

• t distribution (MTD) with location parameter mu and scatter matrix Sigma

This function uses the plot3d.function function.

Usage

plotmvd(mu, Sigma, beta = NULL, nu = NULL,
               distribution = c("mggd", "mcd", "mtd"),
               xlim = c(mu[1] + c(-10, 10)*Sigma[1, 1]),
               ylim = c(mu[2] + c(-10, 10)*Sigma[2, 2]), n = 101,
               xvals = NULL, yvals = NULL, xlab = "x", ylab = "y",
               zlab = "f(x,y)", col = "gray", tol = 1e-6, ...)

Arguments

mu	length 2 numeric vector.
Sigma	symmetric, positive-definite square matrix of order 2.
beta	numeric. If distribution = "mggd", the shape parameter of the MGGD. NULL if dist is "mcd" or "mtd".
nu	numeric. If distribution = "mtd", the degrees of freedom of the MTD. NULL if distribution is "mggd" or "mcd".
distribution	the probability distribution. It can be "mggd" (multivariate generalized Gaussian distribution) "mcd" (multivariate Cauchy) or "mtd" (multivariate t).
xlim, ylim	x-and y- limits.
n	A one or two element vector giving the number of steps in the x and y grid, passed to plot3d.function.
xvals, yvals	The values at which to evaluate x and y. If used, xlim and/or ylim are ignored.
xlab, ylab, zlab	The axis labels.
col	The color to use for the plot. See plot3d.function.
tol	tolerance (relative to largest variance) for numerical lack of positive-definiteness in Sigma, for the estimation of the density. See dmggd, dmcd or dmtd.
...	Additional arguments to pass to plot3d.function.

Value

Returns invisibly the probability density function.

Author(s)

Pierre Santagostini, Nizar Bouhlel

References

E. Gomez, M. Gomez-Villegas, H. Marin. A Multivariate Generalization of the Power Exponential Family of Distribution. Commun. Statist. 1998, Theory Methods, col. 27, no. 23, p 589-600. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/03610929808832115")}

S. Kotz and Saralees Nadarajah (2004), Multivariate t Distributions and Their Applications, Cambridge University Press.

See Also

contourmvd: contour plot of a bivariate generalised Gaussian, Cauchy or t density.

dmggd: Probability density of a multivariate generalised Gaussian distribution.

dmcd: Probability density of a multivariate Cauchy distribution.

dmtd: Probability density of a multivariate t distribution.

Examples

mu <- c(1, 4)
Sigma <- matrix(c(0.8, 0.2, 0.2, 0.2), nrow = 2)

# Bivariate generalised Gaussian distribution
beta <- 0.74
plotmvd(mu, Sigma, beta = beta, distribution = "mggd")


# Bivariate Cauchy distribution
plotmvd(mu, Sigma, distribution = "mcd")

# Bivariate t distribution
nu <- 2
plotmvd(mu, Sigma, nu = nu, distribution = "mtd")

multvardiv documentation built on April 3, 2025, 6:08 p.m.