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On linearly increasing mean residual lifetimes
Donald G. Morrison
Journal:

Journal of Applied Probability / Volume 15 / Issue 3 / September 1978

Published online by Cambridge University Press:

14 July 2016, pp. 617-620

Print publication:

September 1978
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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.

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On linearly increasing mean residual lifetimes