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

## Description

Density, distribution function, quantile function and random generation for the Burr distribution with a and k two parameters.

## Usage

 ```1 2 3 4 5 6 7``` ```rburr(n, a, k) dburr(x, a, k) pburr(q, a, k) qburr(p, a, k) ```

## Arguments

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

## Details

The cumulative Burr distribution is

F(x) = 1-( 1 + (x ^ a) ) ^{- k }, x >0, a >0, k > 0

## Value

dburr gives the density, pburr gives the distribution function, qburr gives the quantile function, and rburr generates random deviates.

The length of the result is determined by n for rburr, 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``` ```plot(function(x) dburr(x,3,1), 0, 5,ylab="density", main = " burr density ") plot(function(x) pburr(x,3,1), 0, 5,ylab="distribution function", main = " burr Cumulative ") plot(function(x) qburr(x,3,1), 0, 1,ylab="quantile", main = " burr Quantile ") #generate a sample of burr distribution of size n n <- 100 x <- rburr(n, 1, 1) ```

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