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

## Description

Density, distribution function, quantile function and random generation for the Pareto distribution (type I).

## Usage

 ```1 2 3 4``` ```dpareto(x, shape, scale = 1, log = FALSE) ppareto(x, shape, scale = 1, lower.tail = TRUE, log.p = FALSE) qpareto(p, shape, scale = 1, lower.tail = TRUE, log.p = FALSE) rpareto(n, shape, scale = 1) ```

## Arguments

 `x` Vector of quantiles. `p` Vector of probabilities. `n` Number of observations. `shape` The shape parameter of the Pareto distribution, a strictly positive number. `scale` The scale parameter of the Pareto distribution, a strictly positive number. Its default value is `1`. `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 Pareto distribution is equal to F(x) = 1-(x/scale)^{-shape} for all x ≥ scale and F(x)=0 otherwise. Both `shape` and `scale` need to be strictly positive.

## Value

`dpareto` gives the density function evaluated in x, `ppareto` the CDF evaluated in x and `qpareto` the quantile function evaluated in p. The length of the result is equal to the length of x or p.

`rpareto` returns a random sample of length n.

## Author(s)

Tom Reynkens.

`tPareto`, `GPD`, `Distributions`
 ```1 2 3 4 5 6 7``` ```# Plot of the PDF x <- seq(1, 10, 0.01) plot(x, dpareto(x, shape=2), xlab="x", ylab="PDF", type="l") # Plot of the CDF x <- seq(1, 10, 0.01) plot(x, ppareto(x, shape=2), xlab="x", ylab="CDF", type="l") ```