# rburr.dependent: Generate Burr dependent data In extremefit: Estimation of Extreme Conditional Quantiles and Probabilities

## Description

Random generation function for the dependent Burr with a, b two shapes parameters and alpha the dependence parameter.

## Usage

 `1` ```rburr.dependent(n, a, b, alpha) ```

## Arguments

 `n` the number of observations. If length(n) > 1, the length is taken to be the number required. `a` a parameter of the function. `b` a parameter of the function. `alpha` the dependence parameter. It is defined by a single value between 0 and 1. The value 1 corresponds to the full independence. The closer to 0 the value of alpha is, the stronger is the dependence. alpha cannot take the value 0.

## Details

The description of the dependence is described in Fawcett and Walshaw (2007). The Burr distribution is : F(x) = 1 - ( 1 + (x ^ a) ) ^ { - b }, x > 0, a > 0, b > 0 where a and b are shapes of the distribution.

## Value

Generates a vector of random deviates. The length of the result is determined by n.

## References

Fawcett, D. and Walshaw, D. (2007). Improved estimation for temporally clustered extremes. Environmetrics, 18.2, 173-188.

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```theta <- function(t){ 1/2*(1/10+sin(pi*t))*(11/10-1/2*exp(-64*(t-1/2)^2)) } n <- 200 t <- 1:n/n Theta <- theta(t) plot(theta) alpha <- 0.6 Burr.dependent <- rburr.dependent(n, 1/Theta, 1, alpha) ```

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