https://hec.hal.science/hal-00542242Scarsini, MarcoMarcoScarsiniGREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche ScientifiqueDipartimento di Scienze Economiche e Aziendali - LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma]Shaked, MosheMosheShakedUniversity of ArizonaOrdering distributions by scaled order statisticsHAL CCSD1987ReliabilityOrder statisticsLifetimeStochastic orderings[SHS.ECO.ECO] Humanities and Social Sciences/Economics and Finance/Economy and decision scienceHaldemann, Antoine2010-12-02 09:54:522023-03-24 14:52:532010-12-02 09:54:52enJournal articles10.1007/BF012586031Motivated by applications in reliability theory, we define a preordering (X sub 1, ..., X sub n) about or less than (k) (Y sub 1, ..., Y sub n) of nonnegative random vectors by requiring the k-th order statistic of a sub 1 X sub 1, ..., a sub n X sub n to be stochastically smaller than the k-th order statistic of a sub 1 Y sub 1, ..., a sub n Y sub n for all choices of a sub i > O, i = 1, 2, ..., n. We identify a class of functions M sub k, n such that X about or less than (k) Y if and only if E phi (X) < E phi (Y) for all phi epsilon M sub k,n. Some preservation results related to the ordering about or less than (k) are obtained. Some examples and applications of the results are given.