# rmcd: Simulate from a Multivariate Cauchy Distribution In mcauchyd: Multivariate Cauchy Distribution; Kullback-Leibler Divergence

 rmcd R Documentation

## Simulate from a Multivariate Cauchy Distribution

### Description

Produces one or more samples from the multivariate (p variables) Cauchy distribution (MCD) with location parameter mu and scatter matrix Sigma.

### Usage

rmcd(n, mu, Sigma, tol = 1e-6)


### Arguments

 n integer. Number of observations. mu length p numeric vector. The location parameter. Sigma symmetric, positive-definite square matrix of order p. The scatter matrix. tol tolerance for numerical lack of positive-definiteness in Sigma (for mvrnorm, see Details).

### Details

A sample from a MCD with parameters \boldsymbol{\mu} and \Sigma can be generated using:

\displaystyle{\mathbf{X} = \boldsymbol{\mu} + \frac{\mathbf{Y}}{\sqrt{u}}}

where \mathbf{Y} is a random vector distributed among a centered Gaussian density with covariance matrix \Sigma (generated using mvrnorm) and u is distributed among a Chi-squared distribution with 1 degree of freedom.

### Value

A matrix with p columns and n rows.

### Author(s)

Pierre Santagostini, Nizar Bouhlel

dmcd: probability density of a MCD.

### Examples

mu <- c(0, 1, 4)
sigma <- matrix(c(1, 0.6, 0.2, 0.6, 1, 0.3, 0.2, 0.3, 1), nrow = 3)
x <- rmcd(100, mu, sigma)
x
apply(x, 2, median)



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