### 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.

Original language | English |
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Pages (from-to) | 61-69 |

Number of pages | 9 |

Journal | Journal of Japan Industrial Management Association |

Volume | 65 |

Issue number | 2 |

Publication status | Published - Jan 1 2014 |

### Keywords

- Hoeffding probability inequality
- Upper bound
- Upper probability

### ASJC Scopus subject areas

- Strategy and Management
- Management Science and Operations Research
- Industrial and Manufacturing Engineering
- Applied Mathematics

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## Cite this

*Journal of Japan Industrial Management Association*,

*65*(2), 61-69.