mev (version 2.1)

shape.lthill: Lower-trimmed Hill estimator for the shape parameter

Description

Given a sample of Pareto-tailed samples (positive tail index), compute the lower-trimmed Hill estimator. If \(k0=k\), the estimator reduces to Hill's estimator for the shape index

Usage

shape.lthill(xdat, k, k0 = k, sorted = FALSE, ...)

Value

a scalar with the shape parameter estimate if k0 is a scalar, otherwise a data frame with columns k0 for the number of exceedances and shape for the tail index.

Arguments

xdat

[numeric] vector of positive observations

k

[integer] number of order statistics for the threshold

k0

[integer] vector of number of largest order statistics, no greater than k

sorted

[logical] if TRUE, data are assumed to be sorted in decreasing order.

...

additional arguments for other routines (notably vectorize)

References

Bladt, M., Albrecher, H. & Beirlant, J. (2020) Threshold selection and trimming in extremes. Extremes, 23, 629-665 . tools:::Rd_expr_doi("10.1007/s10687-020-00385-0")

Examples

# Pareto sample
n <- 200
xdat <- 10/(1 - runif(n)) - 10
shape.lthill(xdat = xdat, k = 100, k0 = 5:100)