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)

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.

Value

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

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

# NOT RUN {
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)


# }