PWM estimator of the generalised Pareto distribution

Hosking and Wallis (1987): k = l1/l2 - 2, sigma = l1 (1 + k) on the excesses' L-moments; Hosking's k is minus the GPD shape xi. PWM over ML because it has lower bias for -0.5 < k < 0.5 and none of ML's convergence failures at exceedance sample sizes (their Sec. 4). Reliable only for k > -0.5 (xi < 0.5, finite variance); outside that the output carries a warning, not a silently untrustworthy number.

Usage

morie_evt_gpd_pwm(x, threshold = NULL)

Arguments

x

raw sample, or excesses when threshold is NULL.

threshold

when given, excesses are formed here.

Value

list: sigma, k_hosking, xi, n_excesses, threshold, mean_excess, reliable, return_level_fn, method.

References

Hosking and Wallis (1987), Technometrics 29:339-349.

Examples

set.seed(1)
morie_evt_gpd_pwm(stats::rexp(200))$xi
#> [1] -0.2286315