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)

Arguments

x, q

Vector of quantiles.

Vector of probabilities.

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]

Value

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

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

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