DEdH (1989) Eq. (1.7): the Hill estimator plus a second-moment
correction, extending validity to ALL real xi. For genuinely heavy
tails the correction converges to zero and DEdH agrees with Hill
– structure, and a test. The logs still need positive data, a
location restriction rather than a tail one.
Usage
morie_evt_dedh(x, k = NULL)
Arguments
- x
sample; the top k+1 order statistics must be positive.
- k
top order statistics; sqrt(n) when NULL.
Value
list: xi, hill_part, correction, M1, M2, se, k, threshold,
n, method.
References
Dekkers, Einmahl and de Haan (1989), Annals of
Statistics 17:1833-1855, Eq. (1.7).
Examples
set.seed(1)
morie_evt_dedh((1 - stats::runif(500))^(-1 / 4), k = 50)$xi
#> [1] 0.06005746
