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

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)

Document Details

Document Type
Technical Report
Publication Date
Sep 20, 1973
Accession Number
AD0768033

Entities

People

  • Nozer Singpurwalla
  • Robert A. Brown

Organizations

  • George Washington University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Data Science
  • Inequalities
  • Information Science
  • Mathematics
  • Order Statistics
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Mathematics or Statistics
  • Regression Analysis.