Convex combination of two U-statistics for testing new better than used

Article type: Research Article

Authors: Pandit, Parameshwar V.^{a; *} | Anuradha, M.P.^b

Affiliations: [a] Department of Statistics, Bangalore University, Bangalore 560 056, India | [b] Department of Statistics, S.K. Arts and H.S.K., Institute Hubli, India

Correspondence: [*] Corresponding author. E-mail: panditpv@yahoo.com.

Abstract: Testing exponentiality against positive ageing has been an active research area during the past three decades. A particular type of positive ageing, namely the new better than used distributions (NBU), is useful in studying replacement policies. Two classes of test statistic for testing exponentiality, both convex combinations of U-statistics, are proposed against the NBU alternative. The asymptotic distributions of the proposed classes are studied. Performance of members of the test classes is studied in terms of Pitman asymptotic relative efficiency in comparison with the tests due to Hollander and Proschan [6], and due to Ahmad [2]. It is observed that the proposed tests are better for certain values of the sub sample size and mixing coefficient.

Keywords: Asymptotic relative efficiency, exponentiality, subsample

DOI: 10.3233/MAS-2007-2307

Journal: Model Assisted Statistics and Applications, vol. 2, no. 3, pp. 165-173, 2007