Several well-known stochastic orderings are defined in terms of iterated integrals of distribution or survival functions. In this note we will provide necessary conditions for some variability orderings of the above type. These conditions will be based on the comparison of mean differences,...

Von Plato (1991) has recently proposed a necessary condition for the infinite extendibility of a partially exchangeable {0, 1}-valued random vector. This paper will prove necessary conditions for the finite extendibility (of any order) of a partially exchangeable process of real-valued (not...

It has been proved (Sklar, 1959, Publ. Inst. Statist. Univ. Paris 8 229-231) that any multivariate distribution function depends on its arguments only through its marginal distributions. An analogous result will be proved in the general framework of probability measures on (Polish) product...

We consider a finite sequence of exchangeable binary random variables and assume that the conditional expected value of each variable is an average of the observed frequency of success and a prior guess. We obtain a representation of the law of the finite sequence as a beta-binomial. In this way...