Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T20:06:36.877Z Has data issue: false hasContentIssue false
  • English
  • Français

On a characterization of the exponential distribution by order statistics

Published online by Cambridge University Press:  14 July 2016

M. Ahsanullah
M. Ahsanullah*
Affiliation:
Empresa Brasileira de Pequisa Agropecuária (EMBRAPA), Brasília, D.F.
Get access Rights & Permissions [Opens in a new window]

Abstract

Let X1, X2, …, Xn be a random sample of size n from a population with probability density function f(x), x >0, and let X1,n < X2,n < … < Xn,n be the associated order statistics. A characterization of the exponential distribution is shown by considering the identical distribution of the random variables nX1,n and (n − i + 1)(X1,n −; Xi–1,n) for one i and one n with 2 ≦ i ≦ n.

Keywords

EXPONENTIAL DISTRIBUTIONCHARACTERIZATIONIDENTICAL DISTRIBUTIONABSOLUTELY CONTINUOUSMONOTONE HAZARD RATEORDER STATISTICSNONNEGATIVE RANDOM VARIABLE
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 4 , December 1976 , pp. 818 - 822
Copyright
Copyright © Applied Probability Trust 1976 

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

Aczél, S. (1966) Lectures on Functional Equations and their Applications. Academic Press, New York.Google Scholar
Ahsanullah, M. (1975) On a characterization of the exponential distribution. Reunião Internacional Comemorativa do 20° Aniversário da Região Brasileira da Sociedade Internacional de Biometria, September 1975.CrossRefGoogle Scholar
Barlow, R. E., Marshall, A. W. and Proschan, F. (1963) Properties of probability distributions with monotone hazard rate. Ann. Math. Statist. 34, 375–389.CrossRefGoogle Scholar
Desu, M. M. (1971) A characterization of the exponential distribution by order statistics. Ann. Math. Statist. 42, 837–838.Google Scholar
Galambos, J. (1975) Characterizations of probability distributions by properties of order statistics I. In Statistical Distributions in Scientific Work, ed. Patil, G. P. et al., Vol. 3. D. Reidel Publishing Company, Dordrecht, Holland, 71–88.Google Scholar
Korz, S. (1974) Characterizations of statistical distribution, a supplement to a recent survey. Int. Statist. Rev. 42, 39–65.Google Scholar
Puri, P. S. and Rubin, H. (1970) A characterization based on absolute differences of two i.i.d. random variables. Ann. Math. Statist. 41, 2113–2122.CrossRefGoogle Scholar
Sethuraman, J. (1965) On a characterization of three limiting type of extremes. Sankhya A 27, 357–374.Google Scholar