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Inequalities for linear combinations of gamma random variables
Author(s) -
Bock M. E.,
Diaconis P.,
Huffer F. W.,
Perlman M. D.
Publication year - 1987
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315257
Subject(s) - mathematics , weibull distribution , statistics , random variable , combinatorics , humanities , philosophy
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.