# Accession Number:

## ADA169940

# Title:

## Ordering Distributions by Scaled Order Statistics.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## ARIZONA UNIV TUCSON DEPT OF MATHEMATICS

# Personal Author(s):

# Report Date:

## 1985-06-01

# Pagination or Media Count:

## 18.0

# 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.

# Subject Categories:

- Statistics and Probability