shape.hill: Hill's estimator of the shape parameter

In lbelzile/mev: Modelling of Extreme Values

Hill's estimator of the shape parameter

Description

Given a sample of positive observations, calculate the tail index or shape parameter. The shape estimate returned is positive.

Usage

shape.hill(xdat, k)

Arguments

xdat	vector of positive observations
kmin	minimum number of upper order statistics (exceedances) for the estimator
kmax	maximum number of upper order statistics (exceedances) for the estimator

Value

a data frame with the number of order statistics k and the shape parameter estimate shape, or a single numeric value if kmin equals kmax.

References

Hill, B.M. (1975). A simple general approach to inference about the tail of a distribution. Annals of Statistics, 3, 1163-1173.

Examples

xdat <- mev::rgp(n = 200, loc = 1, scale = 0.5, shape = 0.5)
shape.hill(xdat)

lbelzile/mev documentation built on June 14, 2025, 6:40 p.m.