%0 Journal Article %T Ordering distributions by scaled order statistics %+ Groupement de Recherche et d'Etudes en Gestion à HEC (GREGH) %+ Dipartimento di Scienze Economiche e Aziendali %+ University of Arizona %A Scarsini, Marco %A Shaked, Moshe %< avec comité de lecture %@ 1432-2994 %J Mathematical Methods of Operations Research %I Springer Verlag %V Vol. 31, N°1 %P pp. A1-A13 %8 1987 %D 1987 %R 10.1007/BF01258603 %K Reliability %K Order statistics %K Lifetime %K Stochastic orderings %Z Humanities and Social Sciences/Economics and Finance/domain_shs.eco.ecoJournal articles %X Motivated 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. %G English %L hal-00542242 %U https://hec.hal.science/hal-00542242 %~ SHS %~ HEC %~ CNRS %~ AO-ECONOMIE