Hostname: page-component-89b8bd64d-x2lbr Total loading time: 0 Render date: 2026-05-05T21:16:23.640Z Has data issue: false hasContentIssue false
  • English
  • Français

On Life Distributions Having Monotone Residual Variance

Published online by Cambridge University Press:  27 July 2009

Ramesh C. Gupta ,
S. N. U. A. Kirmani  and
Robert L. Launer
Ramesh C. Gupta
Affiliation:
University of Maine Orono, Maine 04469
S. N. U. A. Kirmani
Affiliation:
University of Northern Iowa Cedar Falls, Iowa 50614
Robert L. Launer
Affiliation:
U.S. Army Research OfficeResearch Triangle ParkNorth Carolina 27709
Get access Rights & Permissions [Opens in a new window]

Abstract

Launer [6] introduced the class of life distributions having decreasing (increasing) variance residual life, DVRL (IVRL). It is shown that the DVRL (IVRL) distributions are intimately connected to the behavior of the mean residual life function of the equilibrium distribution. Some counter examples are presented to demonstrate the lack of relationship between DVRL (IVRL) and NBUE (new better than used in expectation) (NWUE; new worse than used in expectation) distributions. Finally, we obtain bounds on moments and survival functions of DVRL (IVRL) distributions. These bounds turn out to be improvements on the previously known bounds for decreasing (increasing) mean residual life (DMRL (IMRL)) distributions.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 1 , Issue 3 , July 1987 , pp. 299 - 307
Copyright
Copyright © Cambridge University Press 1987

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.)

Article purchase

Temporarily unavailable

References

1.Barlow, R. E. (1979). Geometry of the total time on test transform. Naval Res. Logist. Quart. 26: 393–402.CrossRefGoogle Scholar
2.Barlow, R. E. & Proschan, F. (1975). Statistical theory of reliability and life testing: Probability models. New York: Holt, Rinehart, and Winston.Google Scholar
3.Gupta, R. C. (1984). Some characterizations of renewal densities with emphasis in reliability. Math. Operationsforsch u. Statist., ser. Statist 15: 571–579.Google Scholar
4.Gupta, R. C. (1987). On the monotonic properties of the residual variance and their applications in reliability. Journal of Statistical Planning and Inference, forthcoming.CrossRefGoogle Scholar
5.Haines, L. & Singpurwalla, N. D. (1974). Some contributions to the stochastic characterization of wear. In Proschan, F. & Serfling, R. J. (eds.), Reliability and biometry: Statistical analysis of lifelength. Philadelphia: Society for Industrial and Applied Mathematics, pp. 47–80.Google Scholar
6.Launer, R. L. (1984). Inequalities for NBUE and NWUE life distributions. Operations Research 32: 660–667.CrossRefGoogle Scholar
7.Marshall, A. W. & Proschan, F. (1972). Classes of distributions applicable in replacement with renewal theory implications. In Lecam, L., Neyman, J., & Scott, E. L. (eds.), Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (vol. 1). Berkeley, CA: University of California Press, pp. 395–415.Google Scholar
8.Ross, S. M. (1983). Stochastic processes. New York: Wiley.Google Scholar