Model selection: some generalized distributions

Abstract

Many models have been used to represent the distributions of random variables in statistics, engineering, business, and the physical and social science. This paper considers two, four-parameter generalized bea distributions that include nearly all the models actually used as special or limiting cases. Properties and the interrelationships among these distributions are considered. Expressions are reported that facilitate parameter estimation and the analysis of associated means, variances, hazard functions and other distributional characteristics. Estimation procedures corresponding to different data types are considered. Maximum likelihood estimation is used and the value of the likelihood function provides and important criterion for model selection. The relative performance of the various models is compared for several data sets.