Exponential-type upper bounds are formulated for the probability that the maximum of the partial sample sums of discrete random variables having finite equispaced support exceeds or differs from the population mean by a specified positive constant. The new inequalities extend the work of Serfling (1974). An example of the results are given to demonstrate their efficacy.
Becnel, Jeremy; Riggs, Kent; and Young, Dean, "Probability Inequalities for the Sum of Random Variables When Sampling Without Replacement" (2013). Faculty Publications. 24.