98-9   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Inequalities for Independent Bernoulli Trials

The suprema $M^*(a)$ of $P(S-ES=a)$ for given $a\in\R$ are determined where $S$ is any sum of independent Bernoulli random variables and $ES$ its expected value. and some more accurate asymptotics and bounds are presented.

Mathematics Subject Classification (1991): 60E15

Keywords: Binomial distribution, Poisson distribution, local limit theorem, large deviation