Maximum likelihood estimation of generalised Pareto parameters

Source: R/frequentist.R

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.

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])
#> $k
#> [1] -0.101175
#> 
#> $a
#> [1] 1.751086
#>