Abstract
Under the reliability NBU/NWU conditions, the exponential distribution is characterized by stochastic ordering properties which link the geometric compound with minimum order statistics or spacings of order statistics. This somewhat answers a question posed by Kakosyan, Klebanov and Melamed (1984,Characterization of Distributions by the Method of intensively Monotone Operators, Springer, New York). We also show the related results based on the residual life in a renewal process and on record values. Finally, some fundamental properties of the NBUC/NWUC classes of life distributions are investigated.
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Hu, CY., Lin, G.D. Characterizations of the exponential distribution by stochastic ordering properties of the geometric compound. Ann Inst Stat Math 55, 499–506 (2003). https://doi.org/10.1007/BF02517803
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DOI: https://doi.org/10.1007/BF02517803