前世的熵
Varentropy of past lifetimes
摘要：
在可靠性理论中，不确定性是用香农熵来度量的。近年来，为了分析这种测度的变异性，人们引入了变熵概念并对其进行了研究。在本文中，我们定义了一个新的概念，变熵的过去寿命分布的不确定性在过去的生活变化。分析了该变熵与相应的过去熵以及可靠性中的其他概念的关系，研究了线性变换和单调变换对变熵的影响，最后，在比例反向风险率模型下，对随机变量的过去变熵进行了计算.
英文摘要：
In Reliability Theory, uncertainty is measured by the Shannon entropy. Recently, in order to analyze the variability of such measure, varentropy has been introduced and studied. In this paper we define a new concept of varentropy for past lifetime distributions as the variability of uncertainty in past lifetime. We analyze the relation of this varentropy with the corresponding past entropy and other concepts of interest in reliability and we study the effect of linear and monotonic transformations on it. Finally, we evaluate past varentropy for random variables following a proportional reversed hazard rate model.
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