Frechet: The Frechet distribution

In TReynkens/ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

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)

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.

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.

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.

Author(s)

Tom Reynkens.

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")

TReynkens/ReIns documentation built on Nov. 9, 2023, 1:29 p.m.