# frechet: The Frechet Distribution In evd: Functions for Extreme Value Distributions

## Description

Density function, distribution function, quantile function and random generation for the Frechet distribution with location, scale and shape parameters.

## Usage

 ```1 2 3 4``` ```dfrechet(x, loc=0, scale=1, shape=1, log = FALSE) pfrechet(q, loc=0, scale=1, shape=1, lower.tail = TRUE) qfrechet(p, loc=0, scale=1, shape=1, lower.tail = TRUE) rfrechet(n, loc=0, scale=1, shape=1) ```

## Arguments

 `x, q` Vector of quantiles. `p` Vector of probabilities. `n` Number of observations. `loc, scale, shape` Location, scale and shape parameters (can be given as vectors). `log` Logical; if `TRUE`, the log density is returned. `lower.tail` Logical; if `TRUE` (default), probabilities are P[X <= x], otherwise, P[X > x]

## Details

The Frechet distribution function with parameters \code{loc} = a, \code{scale} = b and \code{shape} = s is

G(x) = exp{-[(z-a)/b]^(-s)}

for z > a and zero otherwise, where b > 0 and s > 0.

## Value

`dfrechet` gives the density function, `pfrechet` gives the distribution function, `qfrechet` gives the quantile function, and `rfrechet` generates random deviates.

`rgev`, `rgumbel`, `rrweibull`

## Examples

 ```1 2 3 4 5 6 7``` ```dfrechet(2:4, 1, 0.5, 0.8) pfrechet(2:4, 1, 0.5, 0.8) qfrechet(seq(0.9, 0.6, -0.1), 2, 0.5, 0.8) rfrechet(6, 1, 0.5, 0.8) p <- (1:9)/10 pfrechet(qfrechet(p, 1, 2, 0.8), 1, 2, 0.8) ## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ```

### Example output

```[1] 0.25871959 0.09487423 0.05010381
[1] 0.5630712 0.7190122 0.7878127
[1] 10.329571  5.260165  3.813966  3.157788
[1] 2.453427 1.404726 1.324952 2.864454 1.129849 1.156926
[1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
```

evd documentation built on April 25, 2018, 5:04 p.m.