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

`Pareto`, `Distributions`

Examples

 ```1 2 3 4 5 6 7``` ```# Plot of the PDF x = seq(1,10,0.01) plot(x, dtpareto(x, shape=2, endpoint=10), xlab="x", ylab="PDF", type="l") # Plot of the CDF x = seq(1,10,0.01) plot(x, ptpareto(x, shape=2, endpoint=10), xlab="x", ylab="CDF", type="l") ```

Example output

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ReIns documentation built on July 2, 2020, 4:03 a.m.