Two-component mixtures of normal, gamma, and Gumbel distributions for hydrological applications

Abstract

Whether mixtures of distributions are employed as a flexible modeling device to estimate densities or are used to model data thought to arise from several populations, they provide an efficient tool to approximate a distribution. Indeed, mixtures of distributions can model multiple modes, different types of skewness, etc., but they can also be employed to classify observations from heterogeneous data sets. In this paper, we study mixtures of distributions with normal, gamma, and Gumbel components. Moving away from the standard normal setting, gamma mixtures are developed in order to model strictly positive hydrological data and Gumbel mixtures for extreme variates. Since the data analyzed can exhibit dependency through time, we treat both the independent and dependent cases, where the latter is modeled through a Markov process. A fairly unified approach is adopted for the different distributions and the problem is treated from the Bayesian perspective, which enables us to use marginal densities to automatically compare the adequacy of the different models for a given data set. This model-selection framework allows us to formally test the relevance of using mixture models by computing the marginal likelihoods of single distribution models and to verify the presence of a persistence in the time series by comparing independent and identically distributed (IID) and Markovian mixture models. Copyright 2011 by the American Geophysical Union.