基于超熵的加权累积过去不准确度与Kullback-Leibler散度：性质、估计及应用
Weighted cumulative past inaccuracy and Kullback-Leibler divergence based on extropy: properties, estimation, and applications
AI总结：
该研究基于超熵提出WCPEI、WCPED等加权度量指标，推导其理论性质与非参数估计方法，通过模拟验证估计量表现，并将其应用于均匀性检验与图像像素强度分布分析。
AI中文摘要：
本研究基于累积过去超熵，开发了用于度量两个非负寿命分布间差异的加权框架，提出两个度量指标，分别为加权累积过去超熵不准确度（WCPEI）与加权累积过去超熵Kullback-Leibler散度（WCPED），研究中考虑了广义权重函数，并探究了这些指标的多项理论性质。随后构建了基于经验分布函数的非参数估计量，用于加权累积过去超熵不准确度比（WCPEIR），通过针对不同样本量的蒙特卡洛模拟实验，研究了该估计量的有限样本表现。为说明WCPED的实际应用价值，开展了两项应用研究：其一，利用所提散度指标开发了一种基于超熵的均匀性拟合优度检验方法，在多种备择假设下将其检验功效与若干已有的均匀性检验方法进行对比；其二，提出一项图像分析应用，在改变图像分辨率时，利用所提指标评估像素强度分布的变化。该框架进一步扩展至动态场景，通过对指定时间点前可获得的寿命信息进行条件化处理，得到动态加权累积过去超熵不准确度（DWCPEI）与动态加权累积过去超熵散度（DWCPED），推导了它们的理论性质，并提出了对应的非参数估计方法，使用R软件通过模拟研究评估了这些估计量的有限样本表现。
英文摘要：
This study develops a weighted framework for measuring the discrepancy between two nonnegative lifetime distributions through cumulative past extropy. We propose two measures, referred to as the weighted cumulative past extropy inaccuracy (WCPEI) and the weighted cumulative past extropy Kullback-Leibler divergence (WCPED). The generalized weight function is considered in this study. We investigate a number of theoretical properties of these measures. Empirical distribution function-based nonparametric estimator is subsequently constructed for the weighted cumulative past extropy inaccuracy ration (WCPEIR). Its finite-sample behavior is studied through Monte Carlo simulation experiments for different sample sizes. To illustrate the practical relevance of the WCPED, two applications are considered. First, an extropy-based goodness-of-fit procedure for testing uniformity is developed using the proposed divergence measure. Its power is then compared with that of several established uniformity tests under a variety of alternatives. Second, an image analysis application is presented in which the proposed measure is employed to assess changes in the distributions of pixel intensities when the image resolution is altered. The framework is further extended to a dynamic setting by conditioning on the lifetime information available up to a specified time point. This leads to the dynamic weighted cumulative past extropy inaccuracy (DWCPEI) and dynamic weighted cumulative past extropy divergence (DWCPED). Their theoretical properties are derived, and the corresponding nonparametric estimation procedures are proposed. The finite-sample performance of these estimators is evaluated through simulation studies using R software.
