Generalized maximum likelihood Pareto-Poisson estimators for partial duration series

Abstract

his paper considers use of the generalized Pareto (GP) distribution with a Poisson model for arrivals to describe peaks over a threshold. This yields a three- parameter generalized extreme value (GEV) distribution for the annual maximum series. Maximum likelihood estimates of the GP shape parameter • can result in absurd estimates in small samples. These problems are resolved by addition of a prior distribution on • yielding a generalized maximum likelihood estimator. Results show that a three- parameter partial duration series (PDS) analysis yields quantile estimators with the same precision as an annual maximum series (AMS) analysis when the generalized maximum likelihood (GML) GP and GEV estimators are adopted. For • -< 0 the GML quantile estimators with both PDS and AMS have the best performance among the quantile estimators examined (moments, L moments, and GML). The precision of flood quantiles derived from a PDS analysis is insensitive to the arrival rate X, so that a year of PDS data is generally worth about as much as a year of AMS data when estimating the 100-year flood.