In this paper, we consider a shift-dependent measure of generalized cumulative entropy and its dynamic (past) version in the case where the weight is a general non-negative function. Our results include linear transformations, stochastic ordering, bounds and aging classes properties and some relationships with other survival concepts. We also define the conditional weighted generalized cumulative entropy and weighted generalized cumulative Kerridge inaccuracy measure. For these concepts, we obtain some properties and characterization results under suitable assumptions. Finally, we propose an estimator of this shift-dependent measure using empirical approach. In addition, we study large sample properties of this estimator.

中文翻译：

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加权广义累积过去信息度量的扩展

在本文中，在权重是一般的非负函数的情况下，我们考虑广义累积熵及其动态（过去）形式的位移依赖度量。我们的结果包括线性变换，随机排序，界限和老化类别属性以及与其他生存概念的某些关系。我们还定义了条件加权广义累积熵和加权广义累积Kerridge不准确性测度。对于这些概念，我们在适当的假设下获得了一些特性和表征结果。最后，我们使用经验方法提出了这种依赖于位移的测度的估计器。此外，我们研究了该估计量的大样本属性。