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Inequalities for linear combinations of gamma random variables |
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| Authors: | M E Bock P Diaconis F W Huffer M D Perlman |
| Abstract: | We study the behavior of the tail probabilities of weighted averages of certain independently and identically distributed random variables as the weights are varied. We show that the upper and lower tails are smallest when all the weights are equal. Our results apply to exponential, chi-squared, gamma, and Weibull random variables. |
| Keywords: | Schur-convexity of tails linear combinations gamma distribution tail probabilities |