contourmtd {mstudentd}

Contour Plot of the Bivariate t Density

Description

Draws the contour plot of the probability density of the multivariate t distribution with 2 variables with location parameter mu and scatter matrix Sigma.

Usage

contourmtd(nu, mu, Sigma,
                   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 = "Multivariate t density",
                   sub = NULL, nlevels = 10,
                   levels = pretty(zlim, nlevels), tol = 1e-6, ...)

Arguments

nu

numeric. The degrees of freedom.

mu

length 2 numeric vector.

Sigma

symmetric, positive-definite square matrix of order 2. The scatter matrix.

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.

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 dmtd.

...

additional arguments to plot.window, title, Axis and box, typically graphical parameters such as cex.axis.

Value

Returns invisibly the probability density function.

Author(s)

Pierre Santagostini, Nizar Bouhlel

References

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

See Also

dmtd: probability density of a multivariate t density

plotmtd: 3D plot of a bivariate t density.

Examples

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