# plotmcd: Plot of the Bivariate Cauchy Density In mcauchyd: Multivariate Cauchy Distribution; Kullback-Leibler Divergence

 plotmcd R Documentation

## 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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3390/e24060838")}

`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)

``````

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