A full proof of universal inequalities for the distribution function of the binomial law
Abstract
We present a new form and a short full proof of explicit two-sided estimates for the distribution function Fn,p(x) of the binomial law from the paper published by D.Alfers and H.Dinges in 1984. These inequalities are universal (valid for all binomial distribution and all values of argument) and exact (namely, the upper bound for Fn,p(k) is the lower bound for Fn,p(k+1)). By means of such estimates it is possible to bound any quantile of the binomial law by 2 subsequent integers.
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