contourmcd {mcauchyd}

Contour Plot of the Bivariate Cauchy Density

Description

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

Usage

contourmcd(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 Cauchy density",
                   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 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 dmcd.

...

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

N. Bouhlel, D. Rousseau, A Generic Formula and Some Special Cases for the Kullback–Leibler Divergence between Central Multivariate Cauchy Distributions. Entropy, 24, 838, July 2022. doi:10.3390/e24060838

See Also

dmcd: probability density of a multivariate Cauchy density

plotmcd: 3D plot of a bivariate Cauchy density.

Examples

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