Chen Xinyu, Shi Zhenyu, Xie Yuanqi, Zhang Zichen, Cohen Achraf, Pu Shusen
Department of Mathematics and Statistics, University of West Florida, Pensacola, FL 32514, USA.
Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montreal, QC H3A 0C7, Canada.
Entropy (Basel). 2024 Nov 22;26(12):1006. doi: 10.3390/e26121006.
This paper presents a new methodology for generating continuous statistical distributions, integrating the exponentiated odds ratio within the framework of survival analysis. This new method enhances the flexibility and adaptability of distribution models to effectively address the complexities inherent in contemporary datasets. The core of this advancement is illustrated by introducing a particular subfamily, the "Type 2 Gumbel Weibull-G family of distributions". We provide a comprehensive analysis of the mathematical properties of these distributions, including statistical properties such as density functions, moments, hazard rate and quantile functions, Rényi entropy, order statistics, and the concept of stochastic ordering. To test the robustness of our new model, we apply five distinct methods for parameter estimation. The practical applicability of the Type 2 Gumbel Weibull-G distributions is further supported through the analysis of three real-world datasets. These real-life applications illustrate the exceptional statistical precision of our distributions compared to existing models, thereby reinforcing their significant value in both theoretical and practical statistical applications.
本文提出了一种生成连续统计分布的新方法，该方法将指数化优势比整合到生存分析框架中。这种新方法增强了分布模型的灵活性和适应性，以有效应对当代数据集固有的复杂性。通过引入一个特定的子族，即“第二类耿贝尔威布尔 - G分布族”，来说明这一进展的核心内容。我们对这些分布的数学性质进行了全面分析，包括密度函数、矩、风险率和分位数函数等统计性质、雷尼熵、顺序统计量以及随机序的概念。为了测试我们新模型的稳健性，我们应用了五种不同的参数估计方法。通过对三个真实世界数据集的分析，进一步支持了第二类耿贝尔威布尔 - G分布的实际适用性。这些实际应用表明，与现有模型相比，我们的分布具有卓越的统计精度，从而强化了它们在理论和实际统计应用中的重要价值。
