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 , Bernstein , Pinelis , and Bentkus . We also briefly discuss the infinitely divisible distributions case.
"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