ReIns: tGPD – R documentation

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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)

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.

Author(s)

Tom Reynkens

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")

ReIns

Functions from "Reinsurance: Actuarial and Statistical Aspects"

v1.0.10

GPL (>= 2)

Authors

Tom Reynkens [aut, cre] (<https://orcid.org/0000-0002-5516-5107>), Roel Verbelen [aut] (R code for Mixed Erlang distribution, <https://orcid.org/0000-0002-2347-9240>), Anastasios Bardoutsos [ctb] (Original R code for cEPD estimator), Dries Cornilly [ctb] (Original R code for EVT estimators for truncated data), Yuri Goegebeur [ctb] (Original S-Plus code for basic EVT estimators), Klaus Herrmann [ctb] (Original R code for GPD estimator)

Initial release

2020-05-16