tGPD: The truncated generalised Pareto distribution

In TReynkens/ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

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)

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.

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.

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.

Author(s)

Tom Reynkens

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")

TReynkens/ReIns documentation built on Nov. 30, 2024, 3:47 p.m.