阶数为$\alpha$的累积残差Mathai--Haubold熵的非参数推断

中文摘要 AI 辅助

本文研究了阶数为$\alpha$的累积残差Mathai--Haubold熵的性质。随后提出了该熵测度的动态版本，并在可靠性建模框架内考察了其性质。我们证明，阶数为$\alpha$的动态累积残差Mathai--Haubold熵唯一确定生存函数。利用所提出的测度，推导了指数分布和广义帕累托分布的特征化结果。此外，我们基于生存函数的核估计，为阶数为$\alpha$的累积残差Mathai--Haubold熵及其动态对应物开发了非参数估计量。通过蒙特卡洛模拟研究评估了这些估计量的性能。最后，使用两个真实数据集——飞机挡风玻璃的失效时间数据和40个随机选择的机械开关的失效时间数据——说明了所提出的动态估计量的实际相关性。

英文摘要

In this paper, we study the properties of cumulative residual Mathai--Haubold entropy of order $α$. A dynamic version of this entropy measure is then proposed, and its properties are examined within the framework of reliability modeling. We show that the dynamic cumulative residual Mathai--Haubold entropy of order $α$ uniquely determines the survival function. Characterization results for the exponential and generalized Pareto distributions are derived using the proposed measure. Furthermore, we develop nonparametric estimators for the cumulative residual Mathai--Haubold entropy and its dynamic counterpart of order $α$, based on the kernel estimation of the survival function. The performance of these estimators is evaluated through a Monte Carlo simulation study. Finally, the practical relevance of the proposed dynamic estimator is illustrated using two real data; failure-time data from aircraft windshields and failure-time data from 40 randomly selected mechanical switches.

发表机构

• Kuriakose Elias College（库里亚科斯·埃利亚斯学院）
• Indian Statistical Institute, Chennai（印度统计研究所，金奈）

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