alpha_hills: Estimating the Shape Parameter by Hill's Estimator

In ptsuite: Tail Index Estimation for Power Law Distributions

Description

This function uses the Hill's Estimator to estimate the shape parameter of a given set of data. (Nair et al. 2019; Pokorna 2016; Hill 1975) It is especially useful when the data is known not to follow an exact Pareto distribution but the tail of the data does. Thus, the specification of k, the kth largest observation, allows to specify the point from where Pareto-like behavior may be seen. It is also possible to specify the value at which the tail begins. When k=n, the Hill's Estimator returns the same estimate as alpha_mle with a warning notifying the user.

Usage

alpha_hills(dat, k, value = FALSE)

Arguments

dat	vector of observations
k	number of observations / value equal to or greater than to consider for tail
value	(TRUE/FALSE) indicating if the value which is specified in "k" (TRUE)

Value

A list of the following form:

shape

Estimate of the shape parameter of the data

scale

Estimate of the scale parameter of the data (which is taken to be the minimum of the data)

References

Nair J, Wierman A, Zwart B (2019). "The Fundamentals Of Heavy Tails: Properties, Emergence, And Identification." http://users.cms.caltech.edu/ adamw/heavytails.html.

Pokorna M (2016). Estimation and Application of the Tail Index. Bachelor's thesis, Charles University in Prague, Faculty of Social Sciences, Institute of Economic Studies.

Hill B (1975). "A Simple General Approach To Inference About The Tail Of A Distribution."The Annals of Statistics, 3(5), 1163-1174.

Examples

x <- generate_pareto(10000, 5, 2)
alpha_hills(x, 400)

ptsuite documentation built on May 1, 2019, 10:51 p.m.