Abstract
In this paper, using the completeness properties of certain function sequences, several characterization results of symmetric continuous distributions are established based on various information measures properties of order statistics. It is shown that the equality of some common information measures of upper and lower order statistics is a characteristic property of symmetric distributions. These information measures include Shannon entropy, Rényi entropy, Tsallis entropy, cumulative residual (past) entropy, also some common inaccuracy measures. The results can be used to construct goodness-of-fit test for symmetry.
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