00638269

j

00638269 Ahmad, Ibrahim A. A class of statistics useful in testing increasing failure rate average and new better than used life distributions. J. Stat. Plann. Inference 41, No.2, 141-149 (1994). 1994 Elsevier Science B.V. (North-Holland), Amsterdam EN testing for exponentiality asymptotic normality unbiasedness consistency empirical distributions increasing failure rate average new better than used Pitman asymptotic efficiency relative efficiencies numerical example small sample null distribution critical values Monte Carlo Zbl 0519.62088 Zbl 0241.62055

doi:10.1016/0378-3758(94)90159-7

Summary: A class of test statistics is introduced which can be used to test exponentiality against either increasing failure rate average or new better than used alternatives. The tests of the author (unpublished (1974)) and of {\it J. V. Deshpande} [Biometrika 70, 514-518 (1983; Zbl 0519.62088)] for increasing failure rate average and of {\it M. Hollander} and {\it F. Proschan} [Ann. Math. Stat. 43, 1136-1146 (1972; Zbl 0241.62055)] for new better than used are members of this class. It is shown that in the sense of Pitman asymptotic efficiency, neither Ahmad and Deshpande's nor Hollander and Proschan's tests are the best members in the class for some commonly used alternatives. The best members are identified and their relative efficiencies are evaluated. A numerical example is presented and small sample null distribution critical values are given based on Monte Carlo techniques.