ptsuite (version 1.0.0)

alpha_moment: Estimating the Shape Parameter by Method of Moments

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 \(\alpha\) (shape parameter) is greater than or equal to 1 (Brazauskas and Serfling 2000). This function issues a warning if it detects that \(\alpha\) 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

# NOT RUN {
x <- generate_pareto(10000, 5, 2)
alpha_moment(x)
# }