ON CLASSES OF LIFETIME DISTRIBUTIONS WITH UNKNOWN AGE

  • Authors:

  • Gordon E. Willmot;Jun Cai

  • Affiliations:

  • Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1, E-mail: gewillmot@icarus.math.uwaterloo.ca;Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1, E-mail: jcai@icarus.math.uwaterloo.ca

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2000

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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.