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Mathematics

Iosif Pinelis

Selected Works

2016

Articles 1 - 4 of 4

Full-Text Articles in Physical Sciences and Mathematics

Power-Series.Pdf, Iosif Pinelis Oct 2016

Power-Series.Pdf, Iosif Pinelis

Iosif Pinelis

This a comment made on Terence Tao's blog at https://terrytao.wordpress.com/2016/10/18/a-problem-involving-power-series/

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Optimal Binomial, Poisson, And Normal Left-Tail Domination For Sums Of Nonnegative Random Variables, Iosif Pinelis Mar 2016

Optimal Binomial, Poisson, And Normal Left-Tail Domination For Sums Of Nonnegative Random Variables, Iosif Pinelis

Iosif Pinelis

Exact upper bounds on the generalized moments E ƒ (Sn) of sums Sn of independent nonnegative random variables Xi for certain classes Ƒ of nonincreasing functions ƒ are given in terms of (the sums of) the first two moments of the Xi’s. These bounds are of the form Eƒ(η), where the random variable η is either binomial or Poisson depending on whether n is fixed or not. The classes Ƒ contain, and are much wider than, the class of all decreasing exponential functions. As corollaries of these results, optimal in a certain sense …

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Lefttailbounds.Zip, Iosif Pinelis Dec 2015

Lefttailbounds.Zip, Iosif Pinelis

Iosif Pinelis

The zip file pertains to my paper "Optimal binomial, Poisson, and normal left-tail domination for sums of nonnegative random variables" (arXiv:1503.06482v3 [math.PR]). This zip file contains two folders: Mathematica and Reduce(Redlog). The folder Mathematica contains certain Mathematica notebook (.nb) files and their pdf copies. The folder Reduce(Redlog) contains certain log files of sessions in Reduce and .png copies of the sessions.

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Calculations.Zip, Iosif Pinelis Dec 2015

Calculations.Zip, Iosif Pinelis

Iosif Pinelis

The zip file contains Mathematica notebook calculations.nb and its PDF image calculations.pdf, pertaining to my paper "Positive-part moments via the characteristic functions, and more general expressions".

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