Comparison of dispersions of mixtures of ordered distributions. Issue 4 (4th July 2017) - Miziuła, P.
ABSTRACT: In the paper we consider mixtures of unknown stochastically ordered distribution functions according to known mixing distribution functions. We provide optimal lower and upper bounds on ratios of general dispersion measures of such mixtures. The bounds do not depend on the particular form of dispersion measure. We present applications of the results in reliability theory, insurance mathematics, Bayesian statistics, and regression analysis.