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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 42, Fasc. 1,
pages 133 - 141
DOI: 10.37190/0208-4147.00050
Published online 6.6.2022
 

On the monotonicity of tail probabilities

R. Fokkink
S. Papavassiliou
C. Pelekis

Abstract: Let S and X be independent random variables, assuming values in the set of non-negative integers, and suppose further that both expectations ES and EX are integers satisfying ES>EX. We establish a sufficient condition for the tail probability P(S> ES) to be larger than the tail probability P(S+X> E(S+X)), when the mean of S is equal to the mode.

2010 AMS Mathematics Subject Classification: Primary 60G50; Secondary 60E15.

Keywords and phrases: tail comparisons, sums of independent random variables, (negative) binomial distribution, Poisson distribution, Simmons' inequality.

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