On maximal tail probability of sums of nonnegative, independent and identically distributed random variables

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10369122" target="_blank" >RIV/00216208:11320/17:10369122 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.spl.2017.04.024" target="_blank" >http://dx.doi.org/10.1016/j.spl.2017.04.024</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.spl.2017.04.024" target="_blank" >10.1016/j.spl.2017.04.024</a>

Result language
angličtina
Original language name
On maximal tail probability of sums of nonnegative, independent and identically distributed random variables
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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