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February 2010 Some Bounds on the Deviation Probability for Sums of Nonnegative Random Variables Using Upper Polynomials, Moment and Probability Generating Functions
Steven G. From
Missouri J. Math. Sci. 22(1): 23-36 (February 2010). DOI: 10.35834/mjms/1312232718

Abstract

We present several new bounds for certain sums of deviation probabilities involving sums of nonnegative random variables. These are based upon upper bounds for the moment generating functions of the sums. We compare these new bounds to those of Maurer [2], Bernstein [4], Pinelis [16], and Bentkus [3]. We also briefly discuss the infinitely divisible distributions case.

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Steven G. From. "Some Bounds on the Deviation Probability for Sums of Nonnegative Random Variables Using Upper Polynomials, Moment and Probability Generating Functions." Missouri J. Math. Sci. 22 (1) 23 - 36, February 2010. https://doi.org/10.35834/mjms/1312232718

Information

Published: February 2010
First available in Project Euclid: 1 August 2011

zbMATH: 1202.60042
MathSciNet: MR2650059
Digital Object Identifier: 10.35834/mjms/1312232718

Rights: Copyright © 2010 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.22 • No. 1 • February 2010
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