hal-00542242
https://hec.hal.science/hal-00542242
doi:10.1007/BF01258603
[SHS] Sciences de l'Homme et de la Société
[HEC] HEC Paris
[CNRS] CNRS - Centre national de la recherche scientifique
[AO-ECONOMIE] Archives ouvertes de l'Economie
Ordering distributions by scaled order statistics
Scarsini, Marco
Shaked, Moshe
[SHS.ECO.ECO] Humanities and Social Sciences/Economics and Finance/domain_shs.eco.eco
ART
Reliability
Order statistics
Lifetime
Stochastic orderings
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.
1987
en
Mathematical Methods of Operations Research
Springer Verlag