Hostname: page-component-84b7d79bbc-5lx2p Total loading time: 0 Render date: 2024-07-26T18:36:01.540Z Has data issue: false hasContentIssue false
  • English
  • Français

On linearly increasing mean residual lifetimes

Published online by Cambridge University Press:  14 July 2016

Donald G. Morrison
Donald G. Morrison*
Affiliation:
Columbia University
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that the gamma distribution is the unique mixing distribution of exponentials that leads to a linearly increasing mean residual lifetime function. A corollary of this result is that regardless of the mixing process the Pareto distribution is the unique aggregate distribution mixture with this property.

Keywords

GAMMA MIXING OF EXPONENTIALSPARETO DISTRIBUTIONLINEARLY INCREASING MEAN RESIDUAL LIFETIMESRELIABILITY THEORYSOCIAL MOBILITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 15 , Issue 3 , September 1978 , pp. 617 - 620
Copyright
Copyright © Applied Probability Trust 1978 

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.)

References

Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability Life Testing Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
Bartholomew, D. J. (1973) Stochastic Models for Social Processes, 2nd edn. Wiley, New York.Google Scholar
Bryson, C. and Siddiqui, M. M. (1969) Some criteria for aging. J. Amer. Statist. Assoc. 64, 1472–1483.CrossRefGoogle Scholar
Johnson, N. L. and Kotz, S. (1970) Continuous Univariate Distributions-I. Wiley, New York.Google Scholar
Maguire, B. A., Pearson, E. S. and Wynn, A. H. A. (1952) The time intervals between industrial accidents. Biometrika 39, 168–180.CrossRefGoogle Scholar
Muth, E. J. (1977) Reliability models with positive memory derived from the mean residual life function. In Theory and Applications of Reliability, ed. Tsokos, C. P. and Shimi, I. N. Academic Press, New York.Google Scholar
Shanbhag, D. N. (1970) Characterizations for exponential and geometric distributions. J. Amer. Statist. Assoc. 65, 1256–1259.CrossRefGoogle Scholar
Silcock, H. (1954) The phenomenon of labour turnover. J. R. Statist. Soc. A117, 429–440.Google Scholar
Singer, B. H. and Spilerman, S. (1974) Social mobility models for heterogeneous populations. In Sociological Methodology 1973–1974, ed. Costner, H. L. Jossey-Bass, San Francisco.Google Scholar
Swarz, G. B. (1973) The mean residual life function. IEEE Trans. Reliability R 22, 108–109.CrossRefGoogle Scholar
Watson, G. S. and Wells, W. T. (1961) On the possibility of improving the mean useful life of items by eliminating those with short lives. Technometrics 3, 281–298.CrossRefGoogle Scholar