L-moment estimator of the GEV parameters

Hosking (1990): unbiased PWMs, the shape from k ~ 7.8590 c + 2.9554 c^2 with c = 2/(3 + t3) - log2/log3, then scale and location exactly. Hosking's k is MINUS xi – a heavy (Frechet) tail has k < 0 and xi > 0, and conflating them turns every Frechet into a Weibull, so both are returned, named. L-moments over ML because the GEV likelihood is non-regular for xi < -0.5 and loses in the small samples block maxima produce.

Usage

morie_evt_gev_lmoments(block_maxima)

Arguments

block_maxima

one maximum per block.

Value

list: mu, sigma, k_hosking, xi, l1, l2, t3, tail_type, return_level_fn, n_blocks, method.

References

Hosking (1990), JRSS-B 52:105-124; Hosking, Wallis and Wood (1985), Technometrics 27:251-261.

Examples

set.seed(1)
morie_evt_gev_lmoments(5 + 2 * (-log(stats::runif(100)))^(-0.2))$xi
#> [1] 0.09613919