tBurr: The truncated Burr distribution In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

Description

Density, distribution function, quantile function and random generation for the truncated Burr distribution (type XII).

Usage

 1 2 3 4 dtburr(x, alpha, rho, eta = 1, endpoint = Inf, log = FALSE) ptburr(x, alpha, rho, eta = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE) qtburr(p, alpha, rho, eta = 1, endpoint = Inf, lower.tail = TRUE, log.p = FALSE) rtburr(n, alpha, rho, eta = 1, endpoint = Inf)

Arguments

 x Vector of quantiles. p Vector of probabilities. n Number of observations. alpha The α parameter of the truncated Burr distribution, a strictly positive number. rho The ρ parameter of the truncated Burr distribution, a strictly negative number. eta The η parameter of the truncated Burr distribution, a strictly positive number. The default value is 1. endpoint Endpoint of the truncated Burr distribution. The default value is Inf for which the truncated Burr distribution corresponds to the ordinary Burr 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 Burr distribution is equal to F_T(x) = F(x) / F(T) for x ≤ T where F is the CDF of the ordinary Burr distribution and T is the endpoint (truncation point) of the truncated Burr distribution.

Value

dtburr gives the density function evaluated in x, ptburr the CDF evaluated in x and qtburr the quantile function evaluated in p. The length of the result is equal to the length of x or p.

rtburr returns a random sample of length n.

Tom Reynkens.