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ON CLASSES OF LIFETIME DISTRIBUTIONS WITH UNKNOWN AGE

Published online by Cambridge University Press:  31 October 2000

Gordon E. Willmot  and
Jun Cai
Gordon E. Willmot
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1, E-mail: gewillmot@icarus.math.uwaterloo.ca
Jun Cai
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1, E-mail: jcai@icarus.math.uwaterloo.ca
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Abstract

Some class properties of the used better (worse) than aged [UBA (UWA)] and the used better (worse) than aged in expectation [UBAE (UWAE)] classes of lifetime distributions are considered. Relationships with the decreasing (increasing) mean residual lifetime [DMRL (IMRL)] class and the decreasing (increasing) variance residual lifetime [DVRL (IVRL)] class are established. Discrete UBA and UWA distributions are introduced and studied. Characterizations of UBA and UWA distributions are derived by using discrete aging properties of mixed Poisson distributions. Applications of these results to queueing theory and ruin are then considered. In particular, preservation of UBA (UWA) and UBAE (UWAE) under a transform of life distributions is given.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 14 , Issue 4 , October 2000 , pp. 473 - 484
Copyright
© 2000 Cambridge University Press

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