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极端的桥梁:可逆双方向布分布
Cira G Otiniano1, Eduarda B Silva1, Raul Y Matsushita1
1Department of Statistics, University of Brasília, Brasília 70910-900, Brazil.
Entropy (Basel, Switzerland)
|December 23, 2023
概括
一个新的可逆双模格姆贝尔分布模型既最大的和最小的极端. 这种多功能统计工具提供了一个简单的闭式函数,增强了其在金融和极端价值分析中的使用.
科学领域:
- 统计 统计 统计 统计
- 极端价值理论 极端价值理论
- 金融数学 金融数学
背景情况:
- 传统的极端值模型往往侧重于最大值或最小值,限制了它们在需要同时分析两者的场景中的应用.
- 现有的双模格姆贝尔分布缺乏简单的闭式累积分布函数,这给计算带来了挑战.
研究的目的:
- 介绍一个新的三参数可逆双模格姆贝尔分布.
- 提供一个统计学上多功能工具,同时建模最大和最小极端.
- 提高金融,水文和气象等领域的计算适用性.
主要方法:
- 开发一种新型的三参数可逆双模格姆贝尔分布.
- 一个简单的闭式累积分布函数的导数.
- 分布性质的数学表述和图形说明.
- 对风险价值 (VaR) 估计的财务数据的应用.
主要成果:
- 拟议的分发提供了一个封闭形式的CDF,简化了计算.
- 该模型有效地捕捉了同时发生的极端行为 (最大值和最小值).
- 使用财务数据成功估计风险价值 (VaR) 证明了实际效用.
结论:
- 可逆双模格姆贝尔分布是一个计算上具有吸引力和多功能工具,用于极端价值分析.
- 它通过同时处理最大和最小极限来解决现有模型的局限性.
- 该模型显示了其实用性,特别是在金融风险管理方面.
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