contourmcd: Contour Plot of the Bivariate Cauchy Density

In mcauchyd: Multivariate Cauchy Distribution; Kullback-Leibler Divergence

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. \Sexpr[results=rd]{tools:::Rd_expr_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)

mcauchyd documentation built on May 29, 2024, 2:21 a.m.