Sankhya: The Indian Journal of Statistics
2003, Volume 65, Pt. 2, 292--306
Discrete Convex Ordered Lifetimes: Characterization, Equivalence And Applications
M.C. BHATTACHARJEE, New Jersey Institute of Technology, Newark, USA
SUMMARY: We derive a characterization and simple sufficient conditions for equality in distribution of discrete convex-ordered lifetimes. Special cases of our results yield criteria for the corresponding stochastic equivalence in terms of moments, moment generating or, probability generating functions. When one of the ordered pair of lifetimes is geometric, application of our results yield a new characterization of the discrete memoryless geometric distribution among all survival times which are weakly aging as HNBUE. Illustrative applications of our results for comparing discrete time branching processes are indicated.
AMS (1991) subject classification. 60K10, 62E10, 60J80.
Key words and phrases. Discrete lifetimes, convex ordering, equality in distribution, discrete HNBUE property, Galton-Watson processes.