plotmvd function

Plot a Bivariate Density

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.

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.

Returns

Returns invisibly the probability density function.

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")

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. 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.

Author(s)

Pierre Santagostini, Nizar Bouhlel