rburr {AoE} | R Documentation |
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.
rburr(n, gamma, rho)
n |
Sample size. |
gamma, rho |
Parameters of the Burr distribution. |
The parametrization is chosen such that gamma and rho are the extreme-value index and second-order parameter of the distribution, respectively.
A numeric vector of length n
.
# 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")