| 于海芳,刘升华.指数分布END随机变量和的尾概率上界[J].井冈山大学自然版,2025,46(4):10-14 |
| 指数分布END随机变量和的尾概率上界 |
| TAIL PROBABILITY UPPER BOUNDS OF SUMS OF EXPONENTIAL DISTRIBUTED END RANDOM VARIABLES |
| 投稿时间：2025-01-23 修订日期：2025-03-13 |
| DOI：10.3969/j.issn.1674-8085.2025.04.002 |
| 中文关键词: 概率极限理论 END随机变量 尾概率上界 指数分布 加权和 |
| 英文关键词: probability limit theorem END random variables tail probability upper bound exponential distributed weighted sum |
| 基金项目:国家自然科学基金委青年科学基金项目(12301521)；辽宁省教育厅计划项目(JYT20L03) |
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| 中文摘要: |
| 研究在END条件下，深入探讨服从不同指数分布的随机变量和的尾概率上界。首先，基于指数分布的固有特性以及END的理论框架，提出了一种针对随机变量和尾概率的上界估计方法。通过运用指数分布的数学期望和概率母函数，研究得到在END情况下的尾概率上界结果。此外，对这些随机变量进行了加权处理，并结合改进的经典证明方法，推导出两个END随机变量加权和的尾概率上界。这些研究结果不仅为理解END随机变量的行为特征提供了重要的理论支持，也为相关领域的实际应用提供了参考依据。 |
| 英文摘要: |
| This study aims to explore the tail probability upper bounds of sums of random variables following different exponential distributions under the condition of END. First, based on the inherent properties of exponential distributions and the theoretical framework of END, a method for estimating the upper bounds of tail probabilities for random variable sums is proposed. By utilizing the mathematical expectation and probability generating function of exponential distributions, the study derives tail probability upper bounds in various scenarios. Furthermore, this research also addresses the weighted treatment of these random variables, successfully deriving the tail probability upper bounds for the weighted sums of two END random variables through an improved classical proof method. These findings not only provide significant theoretical support for understanding the behavioral characteristics of END random variables but also offer effective references for practical applications in related fields. |
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