A Bayesian study for the comparison of generalized gamma model with its components

Abstract

Generalized gamma distribution offers a flexible family and many of the important lifetime models are obtained as component models by setting its shape parameters to unity. The flexibility of the generalized gamma model, however, occurs at the cost of its increased complexity. The present paper makes a simulation based Bayesian study to have a thorough comparison of the generalized gamma with its components in situations where the given data appear compatible with this family. Of course, if a component model is recommended the latter inferences are quite easy to deal with. The study has been conducted in two stages. First, the generalized gamma family with a scale and two shape parameters is examined to see if one or both of its shape parameters can be set to unity in order that the component models can be looked upon as possible candidates. Second, a threshold parameter added in to the family selected at the first stage is tested against zero to see if there is any desirability of threshold in the model(s). A real data set is considered for the purpose of illustration. The paper proceeds by checking compatibility of the various component models with the given data set and finally compares the models to select the one that is most pertinent with the data. © Indian Statistical Institute 2011.