Conditionally Specified Models: New Developments and Applications

Abstract

In the last years, an important part of Enrique Castillo's research work, has been focused on statistical applications of models with conditional specification. The present paper introduces some new developments and applications of this kind of models to be studied in a near future. Firstly, some new and some old bivariate discrete distributions specified by conditionals are presented. Models of bivariate distributions where one of the conditional distribution is discrete and the other one is continuous have important applications in risk theory and actuarial statistics. In this sense, some of these mixture models are proposed. Certain conditionally specified densities are also shown to provide convenient flexible conjugate prior families in certain multiparameter Bayesian settings. We propose prior distributions in estimating with incomplete count data and in certain hurdle models. Finally, we describe the construction of flexible bivariate continuous distributions based on specification of some prescribed conditional hazard functions.