Sankhya: The Indian Journal of Statistics

2004, Volume 66, Pt. 3, 450--465

Comparison of Random Sums in Some  Integral Orderings and Applications


M.C. Bhattacharjee, New Jersey Institute of Technology, Newark, USA

SUMMARY. Some new order preservation properties of stopped sums of independent nonnegative random variables, when the stopping variable is independent of the summands, is investigated. We show that such randomly stopped sums preserve the stochastic Laplace as well as the integral harmonic mean residual life orders. For the case of Laplace orders, there is a suitable converse for each of the order preservation results. Exponential distributions are characterized within the class of random sums with geometric stopping times, via simple moment conditions on the summand obeying a suitably weak aging hypothesis.

AMS (1991) subject classification}. Primary 60K10; secondary 90B25.

Key words and phrases. Randomly stopped sums, Laplace ordering, exponential distributions.

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