On maximal tail probability of sums of nonnegative, independent and identically distributed random variables
Tomasz Łuczak,
Katarzyna Mieczkowska and
Matas Šileikis
Statistics & Probability Letters, 2017, vol. 129, issue C, 12-16
Abstract:
We consider the problem of finding the optimal upper bound for the tail probability of a sum of k nonnegative, independent and identically distributed random variables with given mean x. For k=1 the answer is given by Markov’s inequality and for k=2 the solution was found by Hoeffding and Shrikhande in 1955. We show that the solution for k=3 as well as for general k, provided x≤1/(2k−1), follows from recent results of extremal combinatorics.
Keywords: I.i.d. random variables; Tail probability; Markov’s inequality (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:129:y:2017:i:c:p:12-16
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DOI: 10.1016/j.spl.2017.04.024
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