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区分功率定律和帕雷托分布之间的区别
Joan Del Castillo1, Pedro Puig1
1Departament de Matemàtiques, Universitat Autònoma de Barcelona, Cerdanyola del Vallès, Spain.
Physical review. E
|July 19, 2023
概括
本研究介绍了位置帕雷托分布,扩展了功率定律分布. 一个概率比测试有效地区分这些模型,特别是当数据显示日志-日志线性时.
科学领域:
- 统计 统计 统计 统计
- 可能性理论概率理论.
- 数据分析 数据分析
背景情况:
- 权力定律分布在各种科学领域被广泛使用.
- 区分电力法和相关的分布可能是具有挑战性的.
- 经典方法在区分类似模型时可能缺乏灵敏度.
研究的目的:
- 介绍位置帕雷托分布作为功率定律分布的自然延伸.
- 开发和评估模型选择的概率比测试.
- 为实证数据选择合适的分布提供指导.
主要方法:
- 位置帕雷托分布的推导.
- 发展一个概率比率测试统计的发展.
- 对分布的统计性质的调查和测试.
- 使用真实世界的数据集进行应用和验证.
主要成果:
- 位置帕雷托分布为电力法分布提供了一个灵活的替代方案.
- 概率比率测试证明了高的区分能力.
- 该测试对于在日志日志尺度上呈现线性数据特别有效.
- 解释了两种模型对于较大的观测值的相似性能.
结论:
- 位置帕雷托分布是统计建模工具的宝贵补充.
- 拟议的概率比测试为模型选择提供了一种简单而强大的方法.
- 该测试建议用于补充累积分布函数在日志日志图中是线性的数据集.
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