In this research a probabilistic model or family of models is assumed and various properties of these models are investigated. Much of the work is concerned with comparisons or orderings of the models and the statistical implications of these orderings. Also the problem of how to choose or specify models is also examined. In particular, problems in tail heaviness, maximal ancillarity and weak completeness are studied. Also tail behavior and modality of ratios as well as ordered families of distributions are investigated.
