Adjusting for small-sample non-normality of design event estimators under a generalized Pareto distribution

- The generalized Pareto distribution (GPD) is considered along with maximum likelihood estimators for its quantiles.
- In hydrology, these quantiles are used as “design events”.
- Hydrologists traditionally use large-sample theory to construct confidence intervals for quantile (CIQs) under a GPD model.
- We show that this large-sample approach leads to inaccurate results.
- An improvement is therefore proposed for these classically obtained CIQs.

SummaryThe generalized Pareto distribution (GPD) is a widely used frequency model for fitting extremes in hydrology, especially to fit exceedances over a threshold in the peaks-over-threshold (POT) modeling of floods or other extreme hydrological phenomena. A key goal in fitting frequency distributions to data is to allow the estimation of distribution quantiles, which in hydrology are often used as “design events”. The maximum likelihood (ML) method is a recommended method for fitting the GPD to data. To provide a measure of the statistical error involved in the estimation of design events, confidence intervals for quantiles (CIQs) have to be calculated. Hydrologists have traditionally used large-sample theory to construct such CIQs, but it is shown in the present study that this leads to inaccurate results for quantiles in the right-tail of a GPD. An improvement is therefore proposed for these classically obtained CIQs under a GPD model fitted by ML. The conventional and proposed approaches are compared through Monte Carlo (MC) simulation, and the resulting recommendations are put to use in a hydrological application.