一个新的阿尔法功率-G家族,使用辅数函数与应用程序和回归建模
Amani S Alghamdi1, Shatha F ALoufi2
1Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia. amaalghamdi@kau.edu.sa.
Scientific reports
|February 17, 2026
概括
研究人员引入了共弦α功率产生的家族,一种新的统计分布. 同位数α功率-韦布尔 (CAP-W) 模型表现出各种形状和危险率的灵活性,通过真实数据分析验证.
科学领域:
- 统计 统计 统计 统计
- 可能性理论概率理论.
- 数学建模的数学建模
背景情况:
- 灵活统计分布的需要对于模拟各种现实世界的现象至关重要.
- 现有的分布家族可能无法捕捉复杂的数据特征,例如变化的危险率.
研究的目的:
- 引入一个新的统计分布家族:共弦α功率生成家族.
- 开发和分析这个家族中的一个特定模型,即代数α权力-韦布尔 (CAP-W) 分布.
- 评估参数估计方法的性能和CAP-W模型在现实应用中的实用性.
主要方法:
- 结合阿尔法功率转换与共弦函数,创建一个新的分布家族.
- 导出协弦值α功率-韦布尔 (CAP-W) 分布的统计性质,包括量子数,雷尼值和顺序统计.
- 使用最大概率,普通最小平方,加权最小平方和克拉梅尔--米塞斯方法进行参数估计.
- 进行模拟研究并将模型应用于四个真实数据集.
主要成果:
- CAP-W分布表现出灵活的密度函数 (右倾,对称,下降) 和各种危险率形状 (J形,浴,增加,减少).
- 参数估计方法显示了通过模拟评估的不同性能.
- CAP-W模型在分析四个现实世界数据集方面表现出有效性.
- 成功开发并应用了对log cosine alpha强的韦布尔回归模型.
结论:
- 同位数α功率产生的家族,特别是CAP-W模型,为统计分布工具包提供了有价值和灵活的补充.
- 拟议的模型及其回归扩展对于分析复杂的现实世界数据是有效的.
- 该研究验证了新分布在统计建模中的实际适用性.
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