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一个扩展的雷利·韦布尔模型与精算测量和应用
Mohammed Elgarhy1,2, Arne Johannssen3, Mohamed Kayid4
1Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62521, Egypt.
Heliyon
|December 13, 2024
概括
这项研究引入了马歇尔-奥尔金-雷利-韦布尔 (MORW) 模型,一种新的统计分布. 这就是MORW模型.
科学领域:
- 统计 统计 统计 统计
- 可能性理论概率理论.
- 可靠性工程可靠性工程
背景情况:
- 雷利-韦布尔分布是生命周期数据的灵活模型.
- 马歇尔-奥尔金分布家族为创建新的,更灵活的分布提供了一种方法.
- 在可靠性和精算科学方面需要先进的统计模型.
研究的目的:
- 提出和分析一个新的统计模型,马歇尔-奥尔金-雷利-韦布尔 (MORW) 分布.
- 导出并讨论MORW分布的各种数学和统计属性.
- 评估MORW模型的不同参数估计方法的性能,并证明其实际实用性.
主要方法:
- 使用马歇尔-奥尔金家族的雷利-韦布尔模型的扩展.
- 分析表达式的导出量数,时刻,和顺序统计.
- 蒙特卡洛模拟来评估估计器的性能.
- 计算精算指标,如风险值和预期缺口.
- 应用到现实世界的数据集进行验证.
主要成果:
- 为MORW分布的关键统计性质得出了明确的公式.
- 通过模拟,对六种估计方法进行了全面的比较.
- MORW模型证明了对真实数据的适用性和有用性.
- 计算了精算指标,突出了风险管理中的潜在应用.
结论:
- 拟议的马歇尔-奥尔金-雷利-韦布尔分布 (MORW) 是统计建模工具包的一个有价值的补充.
- 该研究提供了对MORW模型的彻底理论和经验评估.
- MORW分布对可靠性,精算科学和其他需要灵活寿命建模的领域的应用具有前景.
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