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Concomitants of Generalized Order Statistics from Bivariate Cambanis Family of Distributions Under a General Setting

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Abstract

In this paper, we study the concomitants of m-generalized order statistics (m-GOSs) and m-dual generalized order statistics (m-DGOSs) from bivariate Cambanis family with nonzero parameter values as an extension of several recent papers. Moreover, we derive some information measures, namely the Shannon entropy, Kullback–Leibler (KL) divergence and Fisher information number (FIN) for the concomitants of m-GOSs, when \(m>-1,\) and record values, for \(m=-1.\) Also, the joint distribution of concomitants of m-GOSs and record values for this family are studied. Besides, some useful recurrence relations between moments of concomitants are obtained. Finally, the ordinary order statistics (OOSs), record values and sequential order statistics (SOSs) as subclasses of m-GOSs, as well as the progressive type II censored order statistics (POSs) as a more general subclass of GOSs, are separately discussed.

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Acknowledgements

The authors would like to thank Prof. Rosihan M. Ali Editor in Chief and anonymous referees for their helpful comments, which led to improvements of an earlier version of this paper.

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Authors and Affiliations

  1. School of Computer Science and Technology, Wuhan University of Technology, Wuhan, 430070, China

    M. A. Alawady

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

    M. A. Alawady & H. M. Barakat

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

    M. A. Abd Elgawad

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  1. M. A. Alawady
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  2. H. M. Barakat
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  3. M. A. Abd Elgawad
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Correspondence to M. A. Abd Elgawad.

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Communicated by Anton Abdulbasah Kamil.

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Alawady, M.A., Barakat, H.M. & Abd Elgawad, M.A. Concomitants of Generalized Order Statistics from Bivariate Cambanis Family of Distributions Under a General Setting. Bull. Malays. Math. Sci. Soc. 44, 3129–3159 (2021). https://doi.org/10.1007/s40840-021-01102-1

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