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

Description

Density, distribution function, quantile function and random generation for the truncated Pareto distribution.

Usage

 1 2 3 4 dtpareto(x, shape, scale = 1, endpoint = Inf, log = FALSE) ptpareto(x, shape, scale = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE) qtpareto(p, shape, scale = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE) rtpareto(n, shape, scale = 1, endpoint = Inf)

Arguments

 x Vector of quantiles. p Vector of probabilities. n Number of observations. shape The shape parameter of the truncated Pareto distribution, a strictly positive number. scale The scale parameter of the truncated Pareto distribution, a strictly positive number. Its default value is 1. endpoint Endpoint of the truncated Pareto distribution. The default value is Inf for which the truncated Pareto distribution corresponds to the ordinary Pareto 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(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 Pareto distribution is equal to F_T(x) = F(x) / F(T) for x ≤ T where F is the CDF of an ordinary Pareto distribution and T is the endpoint (truncation point) of the truncated Pareto distribution.

Value

dtpareto gives the density function evaluated in x, ptpareto the CDF evaluated in x and qtpareto the quantile function evaluated in p. The length of the result is equal to the length of x or p.

rtpareto returns a random sample of length n.

Author(s)

Tom Reynkens  