fitGPD {AoE} | R Documentation |
Given a sample of positive observations, the functions fitGPD
and fitPareto
compute the maximum likelihood estimators of the parameters of the (generalized) Pareto distributions.
fitGPD(z) fitPareto(z)
z |
A numeric vector with positive elements. |
The generalized Pareto distribution with shape parameter gamma and scale parameter sigma > 0 is defined by its distribution function
F(z) = 1 - (1 + gamma*z/sigma)^(-1/gamma)
for all z >= 0 such that sigma + gamma*z > 0.
The Pareto distribution with shape parameter alpha > 0 and scale parameter tau > 0 is defined by its distribution function
F(z) = 1 - (1 + z/tau)^(-alpha)
for all z >= 0. It is a reparametrization of the generalized Pareto distribution with positive shape parameter gamma = 1/alpha and scale parameter sigma = tau/alpha.
For fitGPD
, a list with components gamma
and sigma
. For fitPareto
, a list with components alpha
and tau
.
The function fitGPD
is called within the function GPD_par
if its argument method
is set to "ML"
.
Smith, R.L. (1987). Estimating tails of probability distributions. The Annals of Statistics 15, 1174-1207.
# order statistics of random sample of size 100 # from the unit Frechet distribution: x <- sort(- 1/log(runif(100)), decreasing = TRUE) # fit GPD to sample of excesses over 21th largest observation: fitGPD(x[1:20] - x[21])