R: The Frechet Distribution

Frechet {DescTools} | R Documentation

## The Frechet Distribution

### Description

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

### Usage

    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 loc = a, scale = b and 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.

### Author(s)

Alec Stephenson <alec_stephenson@hotmail.com>

### See Also

`rGenExtrVal`, `rGumbel`, `rRevWeibull`

### Examples

    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

[Package DescTools version 0.99.28 Index]