根据多项式定律,某些类型的的非对称分布
Andrea A Rey1, Alejandro C Frery2, Magdalena Lucini3
1Signal and Image Processing Center, Universidad Tecnológica Nacional, Ciudad Autónoma de Buenos Aires C1179AAQ, Argentina.
Entropy (Basel, Switzerland)
|May 27, 2023
概括
这项研究为Rényi和Tsallis和费舍尔信息推导了统计模型,用模拟数据验证它们,并将它们应用于社会调查以进行可靠的比较.
科学领域:
- 信息理论 信息理论
- 统计推理 统计推理
- 量化社会科学 量化社会科学
背景情况:
- 雷尼和萨利斯 entropies是Shannon的概括,对于量化复杂系统中的不确定性至关重要.
- 费舍尔信息测量了一个随机变量对一个未知的参数所携带的信息量.
- 最大概率估计 (MLE) 是用数据估计概率分布的一种标准方法.
研究的目的:
- 从多项样本中使用 MLE 来推导 Rényi 和 Tsallis 输入和 Fisher 信息的非对称分布.
- 开发和验证用于比较不同样本,甚至是不同类别的输入的统计测试.
- 将这些新的统计方法应用于现实世界的社会调查数据.
主要方法:
- 对于选定的信息措施的非对称分布表达式的导出.
- 模拟研究,以验证衍生异常模型的准确性 (包括Tsallis和Fisher的正常近似).
- 开发测试统计数据,用于比较两个样本的输入量.
- 将开发的测试应用于社会调查数据.
主要成果:
- 成功获得了Rényi和Tsallis输入和费舍尔信息的非对称分布.
- 衍生出的非对称模型,特别是Tsallis和费舍尔信息的正常近似,证明与模拟数据相匹配.
- 开发了新的测试统计数据,使得不同类型的可以在样本中进行不同类型的类别数量的比较.
- 对社会调查数据的应用产生了与传统的千平方测试相一致的结果,但比传统的千平方测试更为普遍.
结论:
- 衍生出来的非对称模型为分析雷尼和萨利斯 entropies 和费舍尔信息提供了一个强大的框架.
- 开发的统计测试为经验研究中的比较提供了更灵活和更普遍的方法.
- 这些方法增强了复杂数据的分析,例如在社会调查中发现的数据.
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