A Complete Proof of Universal Inequalities for the Distribution Function of the Binomial Law

By A. M. Zubkov, A. A. Serov. 2013

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Variance-based Regularization with Convex Objectives (2016, methodology): “Noting that marginally N 1 ∼ Bin ( n, 1 − δ 2 ) and using , and we would like to lower bound Letting du denote the standard Gaussian CDF, then Zubkov and Serov [31] show that where D kl ( p || q ) = p log +(1 − p ) log 1 − p 1 − q denotes the binary KL-divergence.”
Improved Inequalities for the Poisson and Binomial Distribution and Upper Tail Quantile Functions (2013, methodology): “Exceptions are the inequality of Bohman (see [1, page 169]), which always overestimates the true Poisson probability, and the expressions recently proposed by Zubkov and Serov for the Binomial distribution [5].”