Weibull 分布与本福德定律
概率论
2016-01-20 v1
摘要
本福德定律指出，许多数据集具有偏向较低首位数字的偏差（约 为 1）。其应用广泛，从设计高效计算机到检测税务、选民和图像欺诈。了解哪些常见概率分布近似服从本福德分布至关重要。我们证明了对于许多参数值，Weibull 分布接近本福德定律，并量化了其偏差。由于 Weibull 分布出现在许多问题中，特别是在生存分析中，我们的结果为本福德行为的普遍性提供了额外的论据。证明采用了泊松求和法，这是解决此类问题的有力技术。
引用
@article{arxiv.1402.5854,
title = {The Weibull Distribution and Benford's Law},
author = {Victoria Cuff and Allison Lewis and Steven J. Miller},
journal= {arXiv preprint arXiv:1402.5854},
year = {2016}
}
备注
Version 1.0, 13 pages, 2 figures. This work was done at the 2010 SMALL REU at Williams College, and a summary of it will appear in Chapter Three of The Theory and Applications of Benford's Law, PUP (to appear, S. J. Miller, editor). Since this work was written many of these results have been independently derived and applied them to internet traffic; see the work of Arshadi and Jahangir [AJ]