contourmvd function

Contour Plot of a Bivariate Density

Contour plot of 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, scatter matrix Sigma and degrees of freedom nu

This function uses the contour function.

contourmvd(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]),
                  zlim = NULL, npt = 30, nx = npt, ny = npt,
                  main = NULL, sub = NULL, nlevels = 10,
                  levels = pretty(zlim, nlevels), tol = 1e-6, ...)

Arguments

• mu: length 2 numeric vector.
• Sigma: symmetric, positive-definite square matrix of order 2. The dispersion matrix.
• 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: character string. The probability distribution. It can be "mggd" (multivariate generalized Gaussian distribution) "mcd" (multivariate Cauchy) or "mtd" (multivariate $t$).
• xlim, ylim: x-and y- limits.
• zlim: z- limits. If NULL, it is the range of the values of the density on the x and y values within xlim and ylim.
• npt: number of points for the discretisation.
• nx, ny: number of points for the discretisation among the x- and y- axes.
• main, sub: main and sub title, as for title. If omitted, the main title is set to "Multivariate generalised Gaussian density", "Multivariate Cauchy density" or "Multivariate t density".
• nlevels, levels: arguments to be passed to the contour 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 plot.window, title, Axis and box, typically graphical parameters such as cex.axis.

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 generalized Gaussian distribution
beta <- 0.74
contourmvd(mu, Sigma, beta = beta, distribution = "mggd")

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

# Bivariate t distribution
nu <- 1
contourmvd(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

plotmvd: 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