Improvement of Performance of Hoeffding Probability Inequality

Abstract

Probability inequalities are known as an effective means to evaluate the upper bound of upper probability for an average of some random variables based on only limited stochastic properties, e.g., expectation, variance, and codomain for each random variable. Among them, Hoeffding probability inequality has been known as one of the best theoretical ways for evaluating the upper bound of upper probability about an average of several random variables based on limited stochastic properties such as expectation, variance and codomain in each random variable. In this study, the authors address a study for essentially improving the performance of Hoeffding probability inequality. In consequence, a new probability inequality with more superior performance than Hoeffding probability inequality is derived.