plotmcd {mcauchyd}

Plot of the Bivariate Cauchy Density

Description

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

Usage

plotmcd(mu, Sigma, 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. The scatter matrix.

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 dmcd.

...

Additional arguments to pass to plot3d.function.

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

contourmcd: contour plot of a bivariate Cauchy density.

plot3d.function: plot a function of two variables.

Examples

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