# Frechet: The Frechet distribution In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

 Frechet R Documentation

## The Frechet distribution

### Description

Density, distribution function, quantile function and random generation for the Fréchet distribution (inverse Weibull distribution).

### Usage

``````dfrechet(x, shape, loc = 0, scale = 1, log = FALSE)
pfrechet(x, shape, loc = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
qfrechet(p, shape, loc = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
rfrechet(n, shape, loc = 0, scale = 1)
``````

### Arguments

 `x` Vector of quantiles. `p` Vector of probabilities. `n` Number of observations. `shape` Shape parameter of the Fréchet distribution. `loc` Location parameter of the Fréchet distribution, default is 0. `scale` Scale parameter of the Fréchet distribution, default is 1. `log` Logical indicating if the densities are given as `\log(f)`, default is `FALSE`. `lower.tail` Logical indicating if the probabilities are of the form `P(X\le x)` (`TRUE`) or `P(X>x)` (`FALSE`). Default is `TRUE.` `log.p` Logical indicating if the probabilities are given as `\log(p)`, default is `FALSE`.

### Details

The Cumulative Distribution Function (CDF) of the Fréchet distribution is equal to `F(x) = \exp(-((x-loc)/scale)^{-shape})` for all `x \ge loc` and `F(x)=0` otherwise. Both `shape` and `scale` need to be strictly positive.

### Value

`dfrechet` gives the density function evaluated in `x`, `pfrechet` the CDF evaluated in `x` and `qfrechet` the quantile function evaluated in `p`. The length of the result is equal to the length of `x` or `p`.

`rfrechet` returns a random sample of length `n`.

### Author(s)

Tom Reynkens.

`tFréchet`, `Distributions`

### Examples

``````# Plot of the PDF
x <- seq(1,10,0.01)
plot(x, dfrechet(x, shape=2), xlab="x", ylab="PDF", type="l")

# Plot of the CDF
x <- seq(1,10,0.01)
plot(x, pfrechet(x, shape=2), xlab="x", ylab="CDF", type="l")

``````

ReIns documentation built on Nov. 3, 2023, 5:08 p.m.