Faculty Publications

Some Results On Normalized Spacings From Restricted Families Of Distributions

Document Type

Article

Keywords

Arrangement increasing functions, Failure rate ordering, Joint likelihood ratio ordering, Majorization, Order statistics, Schur functions, Stochastic ordering

Journal/Book/Conference Title

Journal of Statistical Planning and Inference

Volume

46

Issue

1

First Page

47

Last Page

57

Abstract

It is well known that the normalized spacings of a random sample from a DFR (IFR) distribution are stochastically increasing (decreasing). In this note we strengthen this result to show that if the parent distribution is DFR, the successive normalized spacing increase in the failure rate ordering (which implies stochastic ordering) sense. We also study the joint distribution of the normalized spacings when the parent observations are not necessarily identical. It is shown that when the observations are independent with (possibly different) log-convex densities, the joint distribution of the normalized spacings is arrangement increasing. © 1995.

Department

Department of Mathematics

Original Publication Date

1-1-1995

DOI of published version

10.1016/0378-3758(94)00095-D

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