# Frechet: The Frechet Distribution In RTDE: Robust Tail Dependence Estimation

## Description

Density function, distribution function, quantile function, random generation.

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```dfrechet(x, shape, xmin, log = FALSE) pfrechet(q, shape, xmin, lower.tail=TRUE, log.p = FALSE) qfrechet(p, shape, xmin, lower.tail=TRUE, log.p = FALSE) rfrechet(n, shape, xmin) dufrechet(x, log = FALSE) pufrechet(q, lower.tail=TRUE, log.p = FALSE) qufrechet(p, lower.tail=TRUE, log.p = FALSE) rufrechet(n) ```

## Arguments

 `x, q` vector of quantiles. `p` vector of probabilities. `n` number of observations. If `length(n) > 1`, the length is taken to be the number required. `shape` shape parameter. `xmin` lower bound parameter. `log, log.p` logical; if TRUE, probabilities p are given as log(p). `lower.tail` logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x].

## Details

The Frechet distribution is defined by the following density

f(x) = shape * (x - xmin)^{(-shape-1)} * exp(-(x - xmin)^{(-shape)})

for all x>xmin. The unit Frechet distribution corresponds to `xmin=0` and `shape=1`.

## Value

`dfrechet, dufrechet` give the density, `pfrechet, pufrechet` give the distribution function, `qfrechet, qufrechet` give the quantile function, and `rfrechet, rufrechet` generate random deviates.

The length of the result is determined by `n` for `rfrechet, rufrechet`, and is the maximum of the lengths of the numerical parameters for the other functions.

The numerical parameters other than `n` are recycled to the length of the result. Only the first elements of the logical parameters are used.

## Author(s)

Christophe Dutang

## References

Kotz, S. and Nadarajah, S. (2000), Extreme Value Distributions: Theory and Applications, Imperial College Press.

Beirlant, J., Goegebeur, Y., Teugels, J., Segers (2004), Statistics of Extremes: Theory and Applications, John Wiley and Sons.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```##### # (1) density function x <- seq(0, 5, length=24) cbind(x, dfrechet(x, 1/2, 1/4)) ##### # (2) distribution function cbind(x, pfrechet(x, 1/2, 1/4)) ```

RTDE documentation built on Jan. 8, 2020, 5:09 p.m.