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Characterizations of symmetric distributions based on Rényi entropy

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  • Fashandi, M.
  • Ahmadi, Jafar

Abstract

It is proved that the equality of Rényi entropies of upper and lower order statistics as well as upper and lower k-records is a characteristic property of symmetric distributions. Also, for Farlie–Gumbel–Morgenstern (FGM) family, it is shown that under some conditions the equality of entropies of concomitants of upper and lower order statistics as well as concomitants of upper and lower record values is a characteristic property for the uniform distribution.

Suggested Citation

  • Fashandi, M. & Ahmadi, Jafar, 2012. "Characterizations of symmetric distributions based on Rényi entropy," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 798-804.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:4:p:798-804
    DOI: 10.1016/j.spl.2012.01.004
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    References listed on IDEAS

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    1. Hofmann, Glenn & Balakrishnan, N. & Ahmadi, Jafar, 2005. "Characterization of hazard function factorization by Fisher information in minima and upper record values," Statistics & Probability Letters, Elsevier, vol. 72(1), pages 51-57, April.
    2. Zheng, Gang, 2001. "A characterization of the factorization of hazard function by the Fisher information under Type II censoring with application to the Weibull family," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 249-253, April.
    3. Ahmadi, Jafar & Fashandi, M., 2009. "Some characterization and ordering results based on entropies of current records," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2053-2059, October.
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    Citations

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    Cited by:

    1. Jafar Ahmadi, 2021. "Characterization of continuous symmetric distributions using information measures of records," Statistical Papers, Springer, vol. 62(6), pages 2603-2626, December.
    2. Kumar, Vikas, 2016. "Some results on Tsallis entropy measure and k-record values," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 667-673.
    3. Nanda, Asok K. & Sankaran, P.G. & Sunoj, S.M., 2014. "Rényi’s residual entropy: A quantile approach," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 114-121.
    4. Goel, Ritu & Taneja, H.C. & Kumar, Vikas, 2018. "Measure of entropy for past lifetime and k-record statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 623-631.
    5. Ahmadi, J. & Fashandi, M., 2019. "Characterization of symmetric distributions based on some information measures properties of order statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 141-152.
    6. Mohamed A. Abd Elgawad & Haroon M. Barakat & Metwally A. Alawady & Doaa A. Abd El-Rahman & Islam A. Husseiny & Atef F. Hashem & Naif Alotaibi, 2023. "Extropy and Some of Its More Recent Related Measures for Concomitants of K -Record Values in an Extended FGM Family," Mathematics, MDPI, vol. 11(24), pages 1-25, December.
    7. Ahmadi, Jafar, 2020. "Characterization results for symmetric continuous distributions based on the properties of k-records and spacings," Statistics & Probability Letters, Elsevier, vol. 162(C).
    8. Ahmed M. T. Abd El-Bar & Willams B. F. da Silva & Abraão D. C. Nascimento, 2021. "An Extended log-Lindley-G Family: Properties and Experiments in Repairable Data," Mathematics, MDPI, vol. 9(23), pages 1-15, December.
    9. Kayid, M. & Izadkhah, S., 2015. "Characterizations of the exponential distribution by the concept of residual life at random time," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 164-169.
    10. Sunoj, S.M. & Krishnan, Aswathy S. & Sankaran, P.G., 2018. "A quantile-based study of cumulative residual Tsallis entropy measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 410-421.
    11. Maryam Eskandarzadeh & Antonio Di Crescenzo & Saeid Tahmasebi, 2019. "Cumulative Measure of Inaccuracy and Mutual Information in k -th Lower Record Values," Mathematics, MDPI, vol. 7(2), pages 1-19, February.

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