Generalized maximum likelihood Pareto-Poisson estimators for partial duration series

This 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 ann ual maximum series. Maximum likelihood estimates of the GP shape parameter kappa can result in absurd estimates in small samples. These problems are r esolved by addition of a prior distribution on kappa yielding a generalized maximum likelihood estimator. Results show that a three-parameter partial duration series (PDS) analysis yields quantile estimators with the same pre cision as an annual maximum series (AMS) analysis when the generalized maxi mum likelihood (GML) GP and GEV estimators are adopted. For kappa less than or equal to 0 the GML quantile estimators with both PDS and AMS have the b est 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 lambda, so that a year of PDS data is gener ally worth about as much as a year of AMS data when estimating the 100-year flood.