Frechet {ReIns}R Documentation

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)\log(f), default is FALSE.

lower.tail

Logical indicating if the probabilities are of the form P(Xx)P(X\le x) (TRUE) or P(X>x)P(X>x) (FALSE). Default is TRUE.

log.p

Logical indicating if the probabilities are given as log(p)\log(p), default is FALSE.

Details

The Cumulative Distribution Function (CDF) of the Fréchet distribution is equal to F(x)=exp(((xloc)/scale)shape)F(x) = \exp(-((x-loc)/scale)^{-shape}) for all xlocx \ge loc and F(x)=0F(x)=0 otherwise. Both shape and scale need to be strictly positive.

Value

dfrechet gives the density function evaluated in xx, pfrechet the CDF evaluated in xx and qfrechet the quantile function evaluated in pp. The length of the result is equal to the length of xx or pp.

rfrechet returns a random sample of length nn.

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")


[Package ReIns version 1.0.14 Index]