Historical information in a generalized maximum likelihood framework with partial duration and annual maximum series

Abstract

This paper considers use of historical information with partial duration series (PDS) and annual maximum series (AMS) flood risk models. A generalized Pareto distribution for exceedances over a threshold combined with the Poisson arrival model yields a three-parameter generalized extreme value (GEV) distribution for the AMS. When fitting three-parameter GEV models using generalized maximum likelihood estimators, the average gains from use of historical information are about the same with both AMS and PDS frameworks, though the exact values depend upon the shape parameter κ. The effect of the arrival rate λ is modest. In general, average gains are higher when κ=0.0 as opposed to when -0.3≤κ≤-0.1. When fitting two-parameter models (exponential-Poisson and Gumbel), the average gains are less than those observed with the corresponding three-parameter models with κ=0. Fitting a two-parameter AMS lognormal distribution to lognormal data yielded higher average gains with use of historical information than were obtained with the two-parameter AMS/Gumbel distribution.