A full proof of universal inequalities for the distribution function of the binomial law

2012/07/16 by Andrey M. Zubkov, Zubkov, Andrey M., Alexander A. Serov +1
Mathematics · #60E15 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60E15

paper · pdf · doi:10.48550/arxiv.1207.3838

7 pages; to be published in "Teorija verojatnostei i ee primenenija" (in Rissian)

arxiv created 2012/08/31 · arxiv updated 2012/09/03

Abstract

We present a new form and a short full proof of explicit two-sided estimates for the distribution function F_n,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 F_n,p(k) is the lower bound for F_n,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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