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.

Author(s)

Tom Reynkens.

`Burr`, `Distributions`
 ```1 2 3 4 5 6 7``` ```# Plot of the PDF x <- seq(0, 10, 0.01) plot(x, dtburr(x, alpha=2, rho=-1, endpoint=9), xlab="x", ylab="PDF", type="l") # Plot of the CDF x <- seq(0, 10, 0.01) plot(x, ptburr(x, alpha=2, rho=-1, endpoint=9), xlab="x", ylab="CDF", type="l") ```