Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T07:07:05.821Z Has data issue: false hasContentIssue false
  • English
  • Français

Testing for Harmonic New Better than used in Expectation

Published online by Cambridge University Press:  27 July 2009

S. Rao Jammalamadaka  and
Eun-Soo Lee
S. Rao Jammalamadaka
Affiliation:
Department of Statistics and Applied Probability, University of California, Santa Barbara, California 93106
Eun-Soo Lee
Affiliation:
Statistical Standards Division, National Statistical Office, Seoul, Korea 135-080
Get access Rights & Permissions [Opens in a new window]

Abstract

A statistic for testing the null hypothesis that F is the exponential distribution against the alternative of harmonic new better than used in expectation (HNBUE) is proposed. The asymptotic distribution theory for this statistic is derived under the null hypothesis and asymptotic relative efficiency (ARE) with respect to other competing tests for HNBUE is evaluated. This test is applied to the leukemia data described in Bryson and Siddiqui (1969).

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 12 , Issue 3 , July 1998 , pp. 409 - 416
Copyright
Copyright © Cambridge University Press 1998

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.Aly, E.-E.A.A. (1992). On testing exponentiality against HNBUE alternatives. Statistics and Decisions 10: 239–250.Google Scholar
2.Billingsley, P. (1968). Convergence of pmbabiliry measures. New York: Wiley.Google Scholar
3.Bryson, M.C. & Siddiqui, M.M. (1969). Some criteria for aging. Journal of the American Statistical Association 64: 1472–1483.Google Scholar
4.Fraser, D.A.S. (1975). Nonparametric methods in statistics. New York: Wiley.Google Scholar
5.Hollander, M. & Proschan, F. (1975). Tests for the mean residual life. Biometrika 62: 585–593.CrossRefGoogle Scholar
6.Klefsjö, B. (1983). Testing exponentiality against HNBUE. Scandinavian Journal of Statistics 10: 65–75.Google Scholar
7.Loeve, M. (1963). Probability theory. Princeton: D. Van Nostrand Co.Google Scholar
8.Rao, J.S. & Sethuraman, J. (1975). Weak convergence of empirical distribution functions of random variables subject to perturbations and scale factors. Annals of Statistics 3: 299–313.CrossRefGoogle Scholar
9.Rolski, T. (1975). Mean residual life. Bulletin of the International Statistical Institute 46: 266–270.Google Scholar