grimshaw_gp_mle {revdbayes}

Maximum likelihood estimation of generalised Pareto parameters

Description

Uses the methodology of Grimshaw (1993) to find the MLEs of the parameters of the generalised Pareto distribution, based on a sample of positive values. The function is essentially the same as that made available with Grimshaw (1993), with only minor modifications.

Usage

grimshaw_gp_mle(x)

Arguments

x

A numeric vector containing only positive values, assumed to be a random sample from a generalized Pareto distribution.

Value

A numeric vector of length 2. The estimates of the negated shape parameter k (= -\xi) and the scale parameter a (= \sigma).

References

Grimshaw, S. D. (1993) Computing Maximum Likelihood Estimates for the Generalized Pareto Distribution. Technometrics, 35(2), 185-191. and Computing (1991) 1, 129-133. doi:10.1080/00401706.1993.10485040.

See Also

gp for details of the parameterisation of the GP distribution, in terms of \sigma and \xi.

Examples

u <- quantile(gom, probs = 0.65)
grimshaw_gp_mle((gom - u)[gom > u])