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

 contourmcd R Documentation

## 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")}

`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.