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双变 q - 通用极端值分布:一种比较方法与与气候相关数据的应用
Laila A Al-Essa1, Abdus Saboor2, Muhammad H Tahir3
1Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia.
Heliyon
|December 13, 2024
概括
本研究引入了一种用于建模双变极值数据的新方法,解决了传统方法的局限性. 这种新的技术有效地利用q-泛化极端值分布对相互依赖的极端事件进行建模.
科学领域:
- 统计 统计 统计 统计
- 可能性理论概率理论.
- 极端价值理论 极端价值理论
背景情况:
- 传统的极端价值理论模型使用Gumbel,Fréchet或反向Weibull分布来统变数据.
- 现实世界中的极端事件往往是由具有不对称关系的依赖随机变量引起的.
- 已经提出了像q一般化极端值分布这样的单变量扩展.
研究的目的:
- 开发一种用于建模双变极值数据的新方法.
- 为了解决由独立随机变量产生的相互依赖的双变量观测的建模.
- 引入和验证基于q-泛化极端值模型的新双变分布.
主要方法:
- 使用变量转换技术来建立对双变量数据的支持.
- 开发了一种方法,使用q-泛化极端值概率密度函数来建模相互依存的双变极值.
- 应用该技术来对洪水数据和气候数据进行二元化.
主要成果:
- 成功地概念化并开发了一种用于双变极值建模的新技术.
- 通过使用现实世界的数据,证明了拟议的双变量q-泛化极端值分布的竞争力.
- 建立了一种常规方法来提出新的双变分布及其特殊情况,双变q-Gumbel分布.
结论:
- 拟议的双变量q一般化极端值分布为建模相互依赖的极端事件提供了一种竞争性的方法.
- 开发的技术为分析复杂的双变极值数据提供了一个强大的框架.
- 对洪水和气候数据的应用凸显了新分布的实际实用性.
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