Abstract

In addition to entropy, extropy - the complementary dual of entropy has also gained importance as a measure of information in many areas. Extropy of order statistics, record values and mixed systems, residual extropy properties of k record values, past extropy have been extensively studied in literature. In this paper, we propose length (size) biased shift dependent measures of uncertainty i.e., weighted extropy and weighted residual extropy and study their monotone properties, characterization results, and some other properties in the case of order statistics and k-record values. We also discuss these studies for the past extropy measure.

中文翻译：

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阶统计量和k记录值的加权外向和过去外向

摘要

除了熵之外，熵-熵的互补对偶在许多领域中作为信息的度量也变得越来越重要。有序统计的外向性，记录值和混合系统，k个记录值的剩余外向性，过去的外向性在文献中得到了广泛的研究。在本文中，我们提出了不确定性的长度（大小）与偏移相关的度量，即加权外生性和加权残留外生性，并研究了它们的单调性质，表征结果以及在有序统计和k记录值的情况下的其他一些性质。我们还讨论了过去的外向测度的这些研究。