Confidence intervals and accuracy estimation for heavy-tailed generalized Pareto distributions (Q1775993)

Different methods of confidence interval construction for the parameters \(\gamma\) and \(\sigma\) of the generalized Pareto distribution with CDF \(F(x;\gamma,\sigma)=1-(1-\gamma x/\sigma)^{1/\gamma}\) (for \((1-\gamma x)/\sigma>0\)) are considered. Bootstrap bias-corrected and accelerated (BC\({}_a\)) confidence intervals are compared with likelihood-ratio intervals corrected via the Lawley technique. The author's conclusion is that the simulation study indicates better performance of likelihood based methods in small to moderate sample sizes. Simple profile likelihood methods are recommended for larger samples.