alpha_moment: Estimating the Shape Parameter by Method of Moments

In ptsuite: Tail Index Estimation for Power Law Distributions

Description

This function uses the Method of Moments to estimate the shape parameter of a given set of data. (Rytgaard 1990) The method of moments is only accurate if α (shape parameter) is greater than or equal to 1 (Brazauskas and Serfling 2000). This function issues a warning if it detects that α may be less than 1.

Usage

alpha_moment(dat)

Arguments

dat	vector of observations

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

Rytgaard M (1990). "Estimation In The Pareto Distribution." ASTIN Bulletin: The Journal Of The IAA, 20(2), 201-216.

Brazauskas V, Serfling R (2000). "Robust and Efficient Estimation Of The Tail Index Of A Single-Parameter Pareto Distribution." North American Actuarial Journal, 4, 12-27.

Examples

x <- generate_pareto(10000, 5, 2)
alpha_moment(x)

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