A0388
Title: Inequalities and bounds for order statistics
Authors: Paulo Oliveira - CWT - Turistrader - Sociedade de Desenvolvimento Turistico, Lda (Portugal) [presenting]
Abstract: The lifetime of k-out-n systems is described by order statistics. Stochastic ordering of order statistics is a study exploring shape properties of the underlying base distribution, expressed via stochastic comparison with some reference distributions, that define a hierarchy of classes, characterizing a relaxing chain of shape restrictions on the base distribution. One of the classes is the popular increasing hazard rate family, which may be defined by stochastic comparison with the exponential distribution. The method and results are extended to a broader class comparing distributions with respect to the log-logistic distributions, which also show nice lack-of-memory properties. The inclusion in the proposed classes is also tested. Finally, as a consequence of inclusion in appropriate families of distributions, explicit conditions are still derived for comparing moments of order statistics, and, with an application of the Jenssen inequality, some bounds for suitable exceedance probabilities.
