mev (version 2.1)

shape.hill: 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)

Value

a data frame with the number of order statistics k and the shape parameter estimate shape, or a single numeric value if k is a scalar integer.

Arguments

xdat

vector of positive observations

k

vector of order statistics; if missing, a vector going from 10 to sample size minus one.

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)