extremefit (version 1.0.2)

rburr.dependent: Generate Burr dependent data

Description

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

Usage

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

Value

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

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.

References

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

Examples

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)