# Accession Number:

## AD0768033

# Title:

## Some Inequalities for Concave Functions of Order Statistics from IFR (Increasing Failure Rate) Distributions,

# Descriptive Note:

# Corporate Author:

## GEORGE WASHINGTON UNIV WASHINGTON D C PROGRAM IN LOGISTICS

# Personal Author(s):

# Report Date:

## 1973-09-20

# Pagination or Media Count:

## 16.0

# Abstract:

In the paper the authors consider functions which are the sum of the k largest order statistics in a sample of size n from a continuous distribution F, minus nh, where h is a specified constant. It is proven that such functions are concave in n. If F is an exponential distribution, then for a fixed k the authors obtain that value of n which maximizes the expected value of the function defined above. For F IFR an upper bound is obtained on n and also an upper bound on the maximum of the expected value of the function. Some other inequalities are also obtained. Modified author abstract

# Descriptors:

# Subject Categories:

- Statistics and Probability