单位修改的韦布尔分布和量子回归模型
João Inácio Scrimini1, Cleber Bisognin2, Renata Rojas Guerra2
1Federal University of Santa Maria, Roraima Avenue, 1000, 97105-900 Santa Maria, RS, Brazil.
Anais da Academia Brasileira de Ciencias
|December 11, 2025
概括
本研究引入了一种新的单位概率分布 (UMW),用于分析可持续发展目标 (SDG) 数据. 新型量子回归模型有效地分析了SDG指标和阅读技能,支持优质教育和福祉.
科学领域:
- 统计 统计 统计 统计
- 可能性理论概率理论.
- 可持续发展 可持续发展 可持续发展
背景情况:
- 可持续发展目标 (SDGs) 需要强大的统计方法进行分析.
- 现有的概率分布可能无法在单位间隔 (0,1) 中充分建模数据.
- 修改的韦布尔 (MW) 分布提供了灵活性,但需要适应单位间隔数据.
研究的目的:
- 提出一个新的单位概率分布,即单位修改的韦布尔分布 (UMW).
- 为UMW分布式随机变量开发一个量子回归模型.
- 应用这些方法来建模SDG指标,并评估与教育和健康相关的阅读技能.
主要方法:
- 修改后的韦布尔分布的转换,以创建UMW分布.
- 为UMW分布重新参数化的量子回归模型.
- 最大概率估计 (MLE) 用于参数估计和蒙特卡洛模拟用于评估.
主要成果:
- 已经成功地导出和描述了UMW分布.
- 量子回归模型证明了参数估计的有效性.
- 模拟证实了MLE对UMW模型参数的理想性质.
- 这些方法应用于现实世界的可持续发展目标指标和与阅读障碍相关的阅读技能.
结论:
- UMW分布及其相关的量子回归模型为分析单位间隔数据提供了灵活的框架.
- 这些方法为监测和评估实现可持续发展目标的进展提供了有价值的工具.
- 该研究通过数据分析突出了教育,卫生和可持续发展的相互联系.
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