Ordering Distributions by Scaled Order Statistics.
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1985
- Accession Number
- ADA169940
Entities
People
- Marco Scarsini
- Moshe Shaked
Organizations
- University of Arizona