Ordering properties of convolutions of exponential random variables.(English)Zbl 0967.60017

Summary: Convolutions of independent random variables are usually compared. After a synthetic comparison with respect to hazard rate ordering between sums of independent exponential random variables, we focus on the special case where one sum is identically distributed. So, for a given sum of $$n$$ independent exponential random variables, we deduce the “best” Erlang-$$n$$ bounds, with respect to each of the usual orderings: mean ordering, stochastic ordering, hazard rate ordering and likelihood ratio ordering.

MSC:

 6e+16 Inequalities; stochastic orderings
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