Abstract
In survival or reliability studies, the mean residual life or life expectancy is an important characteristic of the model. Here, we study the limiting behaviour of the mean residual life, and derive an asymptotic expansion which can be used to obtain a good approximation for large values of the time variable. The asymptotic expansion is valid for a quite general class of failure rate distributions—perhaps the largest class that can be expected given that the terms depend only on the failure rate and its derivatives.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bryson, C. and Siddiqui, M. M. (1969). Some criteria for aging,J. Amer. Statist. Assoc.,64, 1472–1483.
Calabria, R. and Pulcini, G. (1987). On the asymptotic behaviour of the mean residual life function,Reliability Engineering,19, 165–170.
Chaubey, Y. P. and Sen, P. K. (1999). On smooth estimation of mean residual life,J. Statist. Plann. Inference,75, 223–236.
Hall, W. J. and Wellner, J. A. (1981). Mean residual life,Proceedings of the International Symposium on Statistics and Related Topics (eds. M. Csörgö, D. A. Dawson, J. N. K. Rao and A. K. M. E. Saleh), 169–184, North Holland, Amsterdam.
Hollander, W. and Proschan, F. (1975). Tests for mean residual life,Biometrika,62, 585–593.
Meilijson, I. (1972). Limiting properties of the mean residual lifetime function,Ann. Math. Statist.,43 (1), 354–357.
Muth, E. J. (1977). Reliability models with positive memory derived from the mean residual life function,Theory and Applications of Reliability, (eds. C. P. Tsokos and I. N. Shimi), 401–434, Academic Press, San Diego, California.
Oakes, D. and Dasu, T. (1990). A note on residual life,Biometrika,77, 409–410.
Rojo, J. (1996). Relationships between pure tail orderings of lifetime distributions and some concepts of residual life,Ann. Instit. Statist. Math.,48 (2), 247–255.
Snyder, C. (1982). Kummer congruences for the coefficients of Hurwitz series,Acta Arith.,XL, 175–191.
Author information
Authors and Affiliations
About this article
Cite this article
Bradley, D.M., Gupta, R.C. Limiting behaviour of the mean residual life. Ann Inst Stat Math 55, 217–226 (2003). https://doi.org/10.1007/BF02530495
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02530495