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Characterization of continuous symmetric distributions using information measures of records

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Abstract

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, Rényi 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.

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Acknowledgements

The author would like to thank AE and the referees for their careful reading and useful comments which improved the paper. This research is supported by a grant from Ferdowsi University of Mashhad [Grant Number 2/52719].

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  1. Department of Statistics, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad, 91775, Iran

    Jafar Ahmadi

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  1. Jafar Ahmadi
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Correspondence to Jafar Ahmadi.

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Ahmadi, J. Characterization of continuous symmetric distributions using information measures of records. Stat Papers 62, 2603–2626 (2021). https://doi.org/10.1007/s00362-020-01206-z

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