In this paper, several characterizations of continuous symmetric distributions are provided. The results are based on the properties of some information measures of k-records. These include cumulative residual (past) entropy, Shannon entropy, Renyi entropy, Tsallis entropy, also some common Kerridge inaccuracy measures. It is proved that the equality of information in upper and lower k-records is a characteristic property of continuous symmetric distributions. Completeness properties of certain function sequences are also used to obtain some characterization results.

中文翻译：

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使用记录的信息度量来表征连续对称分布

在本文中，提供了连续对称分布的几个特征。结果基于 k 记录的某些信息度量的属性。这些包括累积残差（过去）熵、香农熵、仁义熵、Tsallis 熵，以及一些常见的 Kerridge 不准确度量。证明了上下k条记录信息的相等性是连续对称分布的特征。某些函数序列的完备性也被用来获得一些表征结果。