×

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:

60E15 Inequalities; stochastic orderings
PDF BibTeX XML Cite
Full Text: DOI