tFr<U+00E9>chet: The truncated Frechet distribution

Description

Density, distribution function, quantile function and random generation for the truncated Fr<U+00E9>chet 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)

Arguments

Vector of quantiles.

Vector of probabilities.

Number of observations.

shape

Shape parameter of the Fr<U+00E9>chet distribution.

loc

Location parameter of the Fr<U+00E9>chet distribution, default is 0.

scale

Scale parameter of the Fr<U+00E9>chet distribution, default is 1.

endpoint

Endpoint of the truncated Fr<U+00E9>chet distribution. The default value is Inf for which the truncated Fr<U+00E9>chet distribution corresponds to the ordinary Fr<U+00E9>chet 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.

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 \(n\).

Details

The Cumulative Distribution Function (CDF) of the truncated Fr<U+00E9>chet distribution is equal to \(F_T(x) = F(x) / F(T)\) for \(x \le T\) where \(F\) is the CDF of an ordinary Fr<U+00E9>chet distribution and \(T\) is the endpoint (truncation point) of the truncated Fr<U+00E9>chet distribution.

Examples

Run this code

# NOT RUN {
# 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")

# }