ReIns (version 1.0.10)

tGPD: The truncated generalised Pareto distribution

Description

Density, distribution function, quantile function and random generation for the truncated Generalised Pareto Distribution (GPD).

Usage

dtgpd(x, gamma, mu = 0, sigma, endpoint = Inf, log = FALSE)
ptgpd(x, gamma, mu = 0, sigma, endpoint = Inf, lower.tail = TRUE, log.p = FALSE)
qtgpd(p, gamma, mu = 0, sigma, endpoint = Inf, lower.tail = TRUE, log.p = FALSE)
rtgpd(n, gamma, mu = 0, sigma, endpoint = Inf)

Value

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

rtgpd returns a random sample of length \(n\).

Arguments

x

Vector of quantiles.

p

Vector of probabilities.

n

Number of observations.

gamma

The \(\gamma\) parameter of the GPD, a real number.

mu

The \(\mu\) parameter of the GPD, a strictly positive number. Default is 0.

sigma

The \(\sigma\) parameter of the GPD, a strictly positive number.

endpoint

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

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

See Also

tGPD, Pareto, Distributions

Examples

# Plot of the PDF
x <- seq(0, 10, 0.01)
plot(x, dtgpd(x, gamma=1/2, sigma=5, endpoint=8), xlab="x", ylab="PDF", type="l")

# Plot of the CDF
x <- seq(0, 10, 0.01)
plot(x, ptgpd(x, gamma=1/2, sigma=5, endpoint=8), xlab="x", ylab="CDF", type="l")