ReIns (version 1.0.15)

tFrechet: The truncated Frechet distribution

Description

Density, distribution function, quantile function and random generation for the truncated Fréchet distribution.

Usage

dtfrechet(x, shape, loc = 0, scale = 1, endpoint = Inf, log = FALSE)
ptfrechet(x, shape, loc = 0, scale = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE)
qtfrechet(p, shape, loc = 0, scale = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE)
rtfrechet(n, shape, loc = 0, scale = 1, endpoint = Inf)

Value

dtfrechet gives the density function evaluated in \(x\), ptfrechet the CDF evaluated in \(x\) and qtfrechet the quantile function evaluated in \(p\). The length of the result is equal to the length of \(x\) or \(p\).

rtfrechet 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.

endpoint

Endpoint of the truncated Fréchet distribution. The default value is Inf for which the truncated Fréchet distribution corresponds to the ordinary Fréchet distribution.

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 truncated Fréchet distribution is equal to \(F_T(x) = F(x) / F(T)\) for \(x \le T\) where \(F\) is the CDF of an ordinary Fréchet distribution and \(T\) is the endpoint (truncation point) of the truncated Fréchet distribution.

See Also

Fréchet, Distributions

Examples

# Plot of the PDF
x <- seq(1, 10, 0.01)
plot(x, dtfrechet(x, shape=2, endpoint=5), xlab="x", ylab="PDF", type="l")

# Plot of the CDF
x <- seq(1, 10, 0.01)
plot(x, ptfrechet(x, shape=2, endpoint=5), xlab="x", ylab="CDF", type="l")