tGPD: The truncated generalised Pareto distribution In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

Description

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

Usage

 1 2 3 4 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 γ parameter of the GPD, a real number. mu The μ parameter of the GPD, a strictly positive number. Default is 0. sigma The σ 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≤ 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 ≤ 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.

Tom Reynkens