Characterization of -entropy with preference
Characterizations of distributions by moments of order statistics when the sample size is random
We give characterizations of the uniform distribution in terms of moments of order statistics when the sample size is random. Special cases of a random sample size (logarithmic series, geometrical, binomial, negative binomial, and Poisson distribution) are also considered.
Compositional models, Bayesian models and recursive factorization models
Compositional models are used to construct probability distributions from lower-order probability distributions. On the other hand, Bayesian models are used to represent probability distributions that factorize according to acyclic digraphs. We introduce a class of models, called recursive factorization models, to represent probability distributions that recursively factorize according to sequences of sets of variables, and prove that they have the same representation power as both compositional...
Convex orderings for stochastic processes
We consider partial orderings for stochastic processes induced by expectations of convex or increasing convex (concave or increasing concave) functionals. We prove that these orderings are implied by the analogous finite dimensional orderings.