逆单位复合雷利分布:具有在不同领域应用的统计性质.
Hatem E Semary1, Emmanuel W Okereke2, Laxmi Prasad Sapkota3
1Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia.
Scientific reports
|August 8, 2025
概括
引入了一个新的反向单位复合雷利分布 (IUCRD),它提供了灵活的属性,并且在现实数据分析中表现出比现有分布更好的性能.
科学领域:
- 统计 统计 统计 统计
- 可能性分布的概率分布.
- 数学建模的数学建模
背景情况:
- 在统计建模中,对灵活的概率分布的需求是持续的.
- 现有的分布可能无法充分捕捉所有现实数据的复杂性.
- 单位复合雷利分布 (UCRD) 作为开发新分布的基础.
研究的目的:
- 介绍和描述一种新的两参分布:反向单位复合雷利分布 (IUCRD).
- 探索IUCRD的数学属性,包括其量子函数,模式,时刻和重尾性.
- 评估IUCRD与现有分布的性能,使用现实世界的数据集.
主要方法:
- IUCRD是通过UCRD的逆转换获得的.
- 该IUCRD的关键统计属性被数学推导和分析.
- 参数估计方法,包括KE和ML,使用蒙特卡洛模拟进行比较.
- 适合度的良好统计数据用于将IUCRD与真实数据上的其他分布进行比较.
主要成果:
- 该IUCRD表现出灵活的特性,包括单模或非增长的PDF,以及可调节的斜度.
- 危险率函数的IUCRD可以是颠倒的浴形或非下降的.
- 确定KE方法是最好的估计方法,ML是第二个最佳方法.
- 与其他七个分布相比,IUCRD证明了对五个现实世界数据集的优越适应.
结论:
- 反单位复合雷利分布 (IUCRD) 是连续概率分布家族的一个有价值的补充.
- 该IUCRD的灵活性和证明的优越适用性使其成为各种数据分析场景的首选.
- 该研究证实了IUCRD在实际应用中的实用性,优于UCRD和逆指数变量等既定分布.
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