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Concomitants of Generalized Order Statistics from Bivariate Cambanis Family: Some Information Measures

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Abstract

In this paper, we study the concomitants of m-generalized order statistics (m-GOS) from the bivariate Cambanis family as an extension of several recent papers. This study can also be applied to the model of m-dual generalized order statistics (m-DGOS) as a parallel model of m-GOS. Some information measures, namely the Shannon entropy, Kullback-Leibler (KL) distance, and Fisher information number (FIN) for the concomitants of m-GOS, are derived. Furthermore, the joint distribution of concomitants of m-GOS for this family is studied. Besides, some useful recurrence relations between moments of concomitants are obtained. Moreover, the ordinary order statistics (OOS) and an important subclass of sequential order statistics (SOS) as subclasses of m-GOS, as well as the progressive type II censored order statistics (POS) as a more general subclass of GOS, are separately discussed. Finally, an application of these results is given for bivariate generalized exponential distribution.

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Acknowledgements

The authors are very grateful to the Editor in Chief, Professor Majid Soleimani-damaneh, and anonymous referees for their insightful review that enabled the authors to improve the paper significantly.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Benha University, Benha, 13518, Egypt

    Mohamed Ahmed Abd Elgawad

  2. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, 44519, Egypt

    Haroon Mohamed Barakat & Metwally Alsayed Alawady

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  1. Mohamed Ahmed Abd Elgawad
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  2. Haroon Mohamed Barakat
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  3. Metwally Alsayed Alawady
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Correspondence to Metwally Alsayed Alawady.

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Communicated by Ahmad Parsian.

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Abd Elgawad, M.A., Barakat, H.M. & Alawady, M.A. Concomitants of Generalized Order Statistics from Bivariate Cambanis Family: Some Information Measures. Bull. Iran. Math. Soc. 48, 563–585 (2022). https://doi.org/10.1007/s41980-021-00532-8

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