Abstract

The extropy is a measure of information introduced as dual to entropy. It is a shift-independent information measure just as the entropy. We introduce here the notion of weighted extropy, a shift-dependent information measure which gives higher weights to larger values of random variables. We also study the weighted residual and past extropies as weighted versions of extropy for residual and past lifetimes. Bivariate versions extropy and weighted extropy are also described. Several examples are presented through out to illustrate all the concepts introduced here.

中文翻译：

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关于加权外数

摘要

熵是作为熵的对偶引入的信息量度。与熵一样，它是与班次无关的信息度量。我们在这里介绍加权熵的概念，这是一种依赖于移位的信息度量，它为较大的随机变量值赋予更高的权重。我们还研究了加权残差和过去的 extropies，作为残差和过去生命期的 extropy 的加权版本。还描述了双变量版本的 extropy 和加权的 extropy。给出了几个例子来说明这里介绍的所有概念。