Abstract
Probability inequalities are used as a means to evaluate the upper bounds of upper probability for an average of some random variables based on finite stochastic properties, excluding the probability distribution functions of respective random variables. Note that in the case of applying the probability inequality, it is not necessary for the population of each random variable to be identical. Of the existing probability inequalities, Hoeffding probability inequality is highly regarded as an excellent probability inequality from the viewpoint of performance. Hoeffding probability inequality evaluates the upper bounds of upper probability for an average of some random variables based on limited stochastic properties such as expectation, variance and codomain in each random variable. However, we consider that there is a room to improve the performance of Hoeffding probability inequality. In this study, we demonstrate a technique for improving the performance of Hoeffding probability inequality in the case that the population of each random variable is not always identical.
