rburr {AoE}R Documentation

Random number generation of the Burr distribution

Description

Generates a random sample from the Burr distribution with parameters gamma > 0 and rho < 0, defined by its distribution function

F(z) = 1 - (z^(-rho/gamma) + 1)^(1/rho)

for z >= 0.

Usage

rburr(n, gamma, rho)

Arguments

n Sample size.
gamma, rho Parameters of the Burr distribution.

Details

The parametrization is chosen such that gamma and rho are the extreme-value index and second-order parameter of the distribution, respectively.

Value

A numeric vector of length n.

Examples

# rho far away from zero
# ==> fast convergence in domain-of-attraction asymptotics
# ==> estimates are stable as a function of the threshold
x <- rburr(n = 1e4, gamma = 0.5, rho = -1)
Hill(x, k = 10:1e3, ylim = c(0,1), log = "x")
abline(h = 0.5, col = "red")

# rho close to zero
# ==> slow convergence in domain-of-attraction asymptotics
# ==> only the highest thresholds can be used
x <- rburr(n = 1e4, gamma = 0.5, rho = -0.25)
Hill(x, k = 10:1e3, ylim = c(0,1), log = "x")
abline(h = 0.5, col = "red")

[Package AoE version 1.0.1 Index]