离散的Poisson Haq分布具有数学属性和计数数据建模
Abdullah M Alomair1, Faisal Ayyaz2, Saadia Tariq2
1Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa, 31982, Saudi Arabia. ama.alomair@kfu.edu.sa.
Scientific reports
|July 3, 2025
概括
引入了一个新的Poisson Haq (PH) 分布,用于分析过度分散的计数数据. 这种灵活的统计模型在医疗应用中表现出比现有分布更高的性能.
科学领域:
- 统计 统计 统计 统计
- 可能性理论概率理论.
- 生物统计学 生物统计学
背景情况:
- 计数数据经常显示过度分散,违反了标准波桑分布的假设.
- 现有的离散分布可能无法充分捕捉过度分散的医疗计数数据的复杂性.
- 需要灵活的统计模型来分析各种生物和医学计数数据集.
研究的目的:
- 提出一个新的一个参数离散分布,Poisson Haq (PH) 分布.
- 分析过度分散的计数数据集,特别是在医疗环境中.
- 开发和评估基于PH分布的参数回归模型.
主要方法:
- 波桑·哈克分布是作为波桑和哈克随机变量的混合构建的.
- 统计学属性,包括故障率形状 (增加和向上的浴),是衍生的.
- 参数估计是使用时刻方法,最大概率估计和贝叶斯方法进行的,采用马先验.
主要成果:
- PH分布有效地模拟了过分散的计数数据,与Poisson,Poisson瞬间指数和Poisson-XLindley分布相比,显示了更好的合适精度 (较低的AIC和BIC值).
- 模拟研究证实了拟议估计器的性能和行为.
- PH回归模型表明,它很适合住院时间长度数据集.
结论:
- 拟议的Poisson Haq分布为在医学和生物研究中分析过度分散的计数数据提供了一个有价值和灵活的替代方案.
- PH分布及其相关的回归模型提供了更高的准确性和更好的数据拟合能力.
- 该模型的适用性在各种医疗数据集中得到验证,包括传染病和细胞遗传性病变.
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