frechet: 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)

Value

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

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 $$G(z) = \exp\left\{-\left(\frac{z-a}{b}\right)^{-s} \right\}$$ for $z > a$ and zero otherwise, where $b > 0$ and $s > 0$.

Examples

Run this code

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