Heterogeneous Mixture Distributions for Modeling Multisource Extreme Rainfalls

Abstract

Frequency analysis has been widely applied to investigate the behavior and characteristics of hydrometeorological variables. Hydrometeorological variables occasionally show mixture distributions when multiple generating phenomena cause the extreme events to occur. In such cases, a mixture distribution should be applied. Past studies on mixture distributions assumed that they are drawn from the same probability density functions. In fact, many hydrometeorological variables can consist of different types of probability density functions. Research on heterogeneous mixture distributions can lead to improvements in understanding the behavior and characteristics of hydrometeorological variables and in the capacity to model them properly. In the present study heterogeneous mixture distributions are developed to model extreme hydrometeorological events. To fit heterogeneous mixture distributions, the authors present an extension of the metaheuristic maximum likelihood approach. The performance of the parameter estimation method employed was verified through simulation tests. The fits of nonmixture, homogeneous mixture, and heterogeneous mixture distributions were evaluated through the application to a real-world case study of the extreme rainfall events of South Korea. Results indicate that the heterogeneous mixture distribution is a good alternative when sources possessing dissimilar statistical characteristics influence extreme hydrometeorological variables.