ReIns (version 1.0.15)

Frechet: 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)

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 \(n\).

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.

Author

Tom Reynkens.

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.

See Also

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")