Standard Error Estimation for Mixed Flood Distributions with Historic Maxima

• Activity Number: 619
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): John Grego*+ and Phil Yates and Kaiwen Mai
• Companies: University of South Carolina and St. Michael's College and University of South Carolina
• Keywords: Flood frequency ; ECM algorithm ; quantile estimation ; order statistics ; censoring

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, though they actually represent extrema. We review these methods and introduce an approach that treats historical maxima as order statistics, and present an adaption of an ECM algorithm to derive estimates for the finite mixture model. The information matrix is difficult to evaluate, so Meilijson's score-based approximation is used instead. We use the total derivative method to compute standard errors for low-frequency quantiles for both traditional censored data methods and our new approach. The method is demonstrated on annual peak daily flow data using mixtures of lognormal and Gumbel distributions.