关于线性连续 k 中取 n：G 系统的累积剩余熵的研究
A Study on Cumulative Residual Extropy of Linear Consecutive k-out-of-n:G Systems
AI总结：
研究线性连续 k 中取 n：G 系统的累积剩余熵，推导其表达式并研究随机序下行为，建立界与结果，引入动态版本并探讨关系，开发非参数估计程序，通过模拟和真实数据集验证估计器性能。
摘要：
在本文中，我们研究了与线性连续 k 中取 n：G 系统相关的累积剩余熵，该系统在可靠性理论和工程应用中发挥着重要作用。我们首先推导了所提出度量的显式表达式，并研究了累积剩余熵在各种随机序下的行为。此外，还建立了几个界和有意义的特征结果。我们还引入了累积剩余熵的动态版本，并探讨了所提出的动态版本与平均剩余寿命函数之间的关系。从推断的角度，我们开发了一种累积剩余熵的非参数估计程序，并建立了估计器的相应一致性性质。通过在不同参数设置下进行广泛的蒙特卡罗模拟研究，进一步研究了所提出估计器的有限样本性能，并通过一个真实数据集进行了验证。
英文摘要：
In this article, we investigate the cumulative residual extropy associated with linear consecutive k-out-of-n:G systems, which play an important role in reliability theory and engineering applications. We first derive explicit expressions for the proposed measure and examine the behavior of cumulative residual extropy under a variety of stochastic orderings. In addition, several bounds and meaningful results of the characterization are established. Moreover, we also introduced the dynamic version of the cumulative residual extropy and explored the relationship between the proposed dynamic version and the mean residual life function. Fromaninferentialperspective, wedevelopanonparametricestimationprocedure for the cumulative residual extropy and establish the corresponding consistency properties of the estimator. The finite-sample performance of the proposed estimator is further investigated through extensive Monte Carlo simulation studies under different parametric settings and validated through a real dataset.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
