A Note on Detecting “More IFR-ness” Property of Life Distributions

Parameshwar V.Pandit, Sujatha Inginashetty

Department of Statistics, Bangalore University, Bangalore-560056, India.
Department of Statistics, Gulbarga University, Gulbarga, India.

DOI: 10.4236/ojs.2012.24055                

Abstract

In this paper, a problem of testing whether one life distribution possesses ‘more IFR’ property than the other is considered. A new test procedure is proposed and the distribution of the test statistic is studied. The performance of the procedure is evaluated in terms of Pitman asymptotic relative efficiency. The consistency property of the test procedure is established. It is observed that the new procedure is better than the existing procedure in the literature.

Keywords

'More IFR' Property; U-statistic; Pitman ARE

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Proschan, F. and Pyke, R. (1967). Tests for monotone failure rate. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, 3, 293-312.
[2]	Barlow, R.E. and Proschan, F. (1969). A note on tests of monotone failure rate based on incomplete data. Ann. Math. Statist. 40, 595-600. http://dx.doi.org/10.1214/aoms/11776927
[3]	Bickel, P.J. and Doksum, K. (1969). Test for monotone failure rate based on normalized spacings. Ann. Math, Statist. 40, 1216-1235. http://dx.doi.org/10.1214/aoms/1177697498
[4]	Bickel, P.J. (1969). Tests of monotone failure rate II. Ann. Math. Statist. 40, 1250-1260. http://dx.doi.org/10.1214/aoms/1177697498
[5]	Hollander, R.M., Park, D.H. & Proschan, F.(1986).Testing whether F is “more NBU” than is G.Microelectron. Reliab. Vol.26, No.1, pp.39-44. http://dx.doi.org/10.1016/0026-2714(86)90769-9
[6]	Tiwari, R.C. and Zalkikar, J.N. (1988). Testing whether F is “more IFRA than G”. Miroelectron. Reliab. Vol.28, No.5, pp.703-712. http://dx.doi.org/10.1016/0026-2714(88)90006-6
[7]	Lim, J.H., Kim, D.K. and Park, D.H. (2005). Tests for detecting more NBU-ness at specific age. Australian and Newziland J.Stat., Vol 47, No.3,329-337.
[8]	Pandit, P.V. and Gudaganavar, N.V.(2009). On two-sample test for detecting differences in the IFR property of life distributions. African Journal of Mathematical and Computer Science Research, Vol.2(2), 25-29.
[9]	Mugadi,A. R, and Ahmad, I.A. (2010). Classes of statistics for testing exponentiality versus IFR or NBUE alternatives, Vol.62, Nos. 245-246, 17-29.