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ReIns (version 1.0.10)

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

x

Vector of quantiles.

p

Vector of probabilities.

n

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(Xx) (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 FT(x)=F(x)/F(T) for xT 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.

See Also

Fr<U+00E9>chet, Distributions

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")

# }

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