Informational dynamics of censored observations

The analysis of stochastic models is often greatly complicated if there are censored observations of the random variables. This paper characterizes families of distributions which help keep tractable the analysis of such models. The present primary motivation is to provide guidance to practitioners in the selection of distributions: If a modeler feels that no member of the families characterized is a reasonable approximation, then he will almost surely encounter serious analytic and computational problems if his data include censored observations. The paper characterizes a family of distributions for which there exist fixed-dimensional sufficient statistics of purely censored observations. It also characterizes an important subset of this family, appropriate for situations where data include both censored and exact observations. The paper derives the corresponding predictive distributions using arbitrary priors and presents some general results relating stochastic dominance among predictive distributions to the parameters of the prior. It also analyzes the cases of discrete and mixed random variables.