# Pareto-Distribution: Pareto distribution In extremefit: Estimation of Extreme Conditional Quantiles and Probabilities

## Description

Density, distribution function, quantile function and random generation for the Pareto distribution where a, loc and scale are respectively the shape, the location and the scale parameters.

## Usage

 ```1 2 3 4 5 6 7``` ```ppareto(q, a = 1, loc = 0, scale = 1) dpareto(x, a = 1, loc = 0, scale = 1) qpareto(p, a = 1, loc = 0, scale = 1) rpareto(n, a = 1, loc = 0, scale = 1) ```

## Arguments

 `q` a vector of quantiles. `a` a vector of shape parameter of the Pareto distribution. `loc` a vector of location parameter of the Pareto distribution. `scale` a vector of scale parameter of the Pareto distribution. `x` a vector of quantiles. `p` a vector of probabilities. `n` a number of observations. If length(n) > 1, the length is taken to be the number required.

## Details

If shape, loc or scale parameters are not specified, the respective default values are 1, 0 and 1.

The cumulative Pareto distribution is

F(x) = 1- ((x-loc)/scale) ^ {-a}, x > loc, a > 0, scale > 0

where a is the shape of the distribution.

The density of the Pareto distribution is

f(x) = (((x-loc)/scale)^( - a - 1) * a/scale) * (x-loc >= scale), x > loc, a > 0, scale > 0

## Value

dpareto gives the density, ppareto gives the distribution function, qpareto gives the quantile function, and rpareto generates random deviates.

The length of the result is determined by n for rpareto, and is the maximum of the lengths of the numerical arguments for the other functions.

The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```par(mfrow = c(3,1)) plot(function(x) dpareto(x), 1, 5,ylab="density", main = " Pareto density ") plot(function(x) ppareto(x), 1, 5,ylab="distribution function", main = " Pareto Cumulative ") plot(function(x) qpareto(x), 0, 1,ylab="quantile", main = " Pareto Quantile ") #generate a sample of pareto distribution of size n n <- 100 x <- rpareto(n) ```

extremefit documentation built on May 6, 2019, 1:10 a.m.