rmcd | R Documentation |

Produces one or more samples from the multivariate (`p`

variables) Cauchy distribution (MCD)
with location parameter `mu`

and scatter matrix `Sigma`

.

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

`n` |
integer. Number of observations. |

`mu` |
length |

`Sigma` |
symmetric, positive-definite square matrix of order |

`tol` |
tolerance for numerical lack of positive-definiteness in Sigma (for |

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.

A matrix with `p`

columns and `n`

rows.

Pierre Santagostini, Nizar Bouhlel

`dmcd`

: probability density of a MCD.

```
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)
```

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