Given a finite set of unobservable independent random variables, assume one can observe their sum, and denote with s its value. Efron, in 1965, described conditions on the involved variables such that each of them stochastically increases in the value s according to the usual stochastic order, i.e., such that the expected value of any non-decreasing function of the variable increases as s increases. The talk deals with recent generalizations of this monotonicity property for the case of dependent summands, and for the stronger likelihood ratio stochastic monotonicity, in the bivariate and in the multivariate cases. A discussion about the effects of positive (negative) dependence among the summands will be part of the talk.
The talk is based on joint works with J. Navarro (Universidad de Murcia) and P. Ortega-Jiménez, M. A. Sordo and A. Súarez-Llorens (Universidad de Cádiz)