ReIns: Frechet – R documentation

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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)

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≤ 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 ≥ 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.

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")

ReIns

Functions from "Reinsurance: Actuarial and Statistical Aspects"

v1.0.10

GPL (>= 2)

Authors

Tom Reynkens [aut, cre] (<https://orcid.org/0000-0002-5516-5107>), Roel Verbelen [aut] (R code for Mixed Erlang distribution, <https://orcid.org/0000-0002-2347-9240>), Anastasios Bardoutsos [ctb] (Original R code for cEPD estimator), Dries Cornilly [ctb] (Original R code for EVT estimators for truncated data), Yuri Goegebeur [ctb] (Original S-Plus code for basic EVT estimators), Klaus Herrmann [ctb] (Original R code for GPD estimator)

Initial release

2020-05-16