Model selection for environmental data

Abstract

A practical approach is proposed for model selection and discrimination among nested and non-nested probability distributions. Some existing problems with traditional model selection approaches are addressed, including standard testing of a null hypothesis against a more general alternative and the use of some well-known discrimination criteria for non-nested distributions. A generalized information criterion (GIC) is used to choose from two or more model structures or probability distributions. For each set of random samples, all model structures that do not perform significantly worse than other candidates are selected. The two-and three-parameter gamma, Weibull and lognormal distributions are used to compare the discrimination procedures with traditional approaches. Monte Carlo experiments are empIoyed to examine the performances of the criteria and tests over large sets of finite samples. For each distribution, the Monte Carlo procedure is undertaken for various representative sets of parameter values which are encountered in fitting environmental quality data.