Abstract

In this work, we propose weighted cumulative Tsallis residual and past entropy measures and their dynamic versions. The properties of the proposed entropy measures are studied. It is shown that the residual entropy uniquely determines the survival function. Characterizations for Rayleigh and Power distributions are obtained based on the proposed entropy measures. The empirical versions of the residual and past entropies are provided and their asymptotic behaviors are discussed. It is shown that the weighted cumulative Tsallis entropy can be used as a risk measure. A dataset is analyzed for illustrative purposes.

中文翻译：

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关于加权累积 Tsallis 残差和过去的熵度量

摘要

在这项工作中，我们提出了加权累积 Tsallis 残差和过去的熵度量及其动态版本。研究了所提出的熵度量的属性。结果表明，残差熵唯一地决定了生存函数。瑞利分布和功率分布的特征是基于所提出的熵度量获得的。提供了剩余熵和过去熵的经验版本，并讨论了它们的渐近行为。结果表明，加权累积 Tsallis 熵可以用作风险度量。出于说明目的分析数据集。