Abstract
Convolutions of independent random variables are usually compared. In this paper, 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.
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Bon, JL., Pãltãnea, E. Ordering Properties of Convolutions of Exponential Random Variables. Lifetime Data Anal 5, 185–192 (1999). https://doi.org/10.1023/A:1009605613222
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DOI: https://doi.org/10.1023/A:1009605613222