Standard error estimation for mixed flood distributions with historic maxima

Abstract

Flood frequency data from multiple sources can be modeled using finite mixture models of stationary distributions. Historic flood data can be incorporated into this framework using censored data methods. Most estimation methods treat historical flood records as typical realizations from the underlying distribution, although they can actually represent extrema. A review of these methods in a finite mixture framework and introduction of an approach that treats historical maxima as order statistics are presented as adaptations of an expectation conditional maximization algorithm to derive estimates for the finite mixture model. When information matrices are difficult to computse, Meilijson's (1989) score‐based approximation is used instead. The total derivative method is used to compute standard errors for low‐frequency quantiles for both traditional censored data methods and the new approach. The method is demonstrated on annual peak flow data using mixtures of lognormal and Gumbel distributions. Copyright © 2015 John Wiley & Sons, Ltd.