Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-06T04:02:55.083Z Has data issue: false hasContentIssue false
  • English
  • Français

Characterization of certain populations by independence of order statistics

Published online by Cambridge University Press:  14 July 2016

János Galambos
János Galambos*
Affiliation:
Temple University, Philadelphia
Get access Rights & Permissions [Opens in a new window]

Abstract

A method, making use of characteristic functions, is presented to prove theorems on characterization of distributions by independence of order statistics. Since exact independence in practice is rarely achieved, much attention is being given in the literature to theorems on determining the distributions for which certain statistics are ‘almost’ independent. The technique of this new line of investigation is strongly dependent on the fact that for the case of exact independence there is a solution in terms of characteristic functions. The present work was guided by this fact. In addition to the new method, Theorem 2 appears to be new.

Keywords

CHARACTERIZATIONPOPULATIONINDEPENDENCEORDER STATISTICSCHARACTERISTIC FUNCTIONSABSOLUTELY CONTINUOUSEXPECTATIONDENSITY FUNCTIONBOREL MEASURABLE FUNCTIONFISZ'S THEOREM; LINEAR TRANSFORMATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 9 , Issue 1 , March 1972 , pp. 224 - 230
Copyright
Copyright © Applied Probability Trust 1972 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Basu, A. P. (1965) On characterization of the exponential distribution by order statistics. Ann. Inst. Statist. Math. Tokyo 17, 93–96.Google Scholar
[2] Crawford, G. B. (1966) Characterization of geometric and exponential distributions. Ann. Math. Statist. 37, 1790–1795.Google Scholar
[3] Epstein, B. and Sobel, M. (1953) Life testing. J. Amer. Statist. Assoc. 48, 486–502.Google Scholar
[4] Ferguson, T. S. (1964) A characterization of the exponential distribution. Ann. Math. Statist. 35, 1199–1207.Google Scholar
[5] Fisz, M. (1958) Characterization of some probability distributions. Skand. Aktuarietidskr. 1–2, 65–70.Google Scholar
[6] Lukacs, E. and Laha, R. G. (1964) Applications of Characteristic Functions. Charles Griffin, London.Google Scholar
[7] Rényi, A. (1953a) A rendezett minták elméletéröl. Magyar Tud. Akad. Mat. Fiz. Oszt. Közl. 3, 467–503.Google Scholar
[8] Rényi, A. (1953b) On the thory of order statistics. Acta Math. Acad. Sci. Hung. 4, 191–231.CrossRefGoogle Scholar
[9] Rogers, G. S. (1963) An alternative proof of the characterization of the density AxB. Amer. Math. Monthly 70, 857–858.Google Scholar