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Concomitants of Ordered Variables from Huang–Kotz FGM Type Bivariate Generalized Exponential Distribution

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Abstract

We introduce the Huang–Kotz Morgenstern type bivariate generalized exponential distribution. Some distributional properties of concomitants of order statistics as well as record values for this family are studied. Recurrence relations between single and product moments of concomitants are obtained. Moreover, the rank and the asymptotic behavior of concomitants of order statistics are investigated.

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References

  1. Ahsanullah, M.: Records and concomitants. Bull. Malays. Math. Sci. Soc. 32(2), 101–117 (2009)

    MathSciNet  MATH  Google Scholar 

  2. Ahsanullah, M., Shakil, M.: Characterizations of Rayleigh distribution based on order statistics and record values. Bull. Malays. Math. Sci. Soc. 36(3), 625–635 (2013)

    MathSciNet  MATH  Google Scholar 

  3. Ahsanullah, M., Shakil, M., Kibria, G.M.: A note on a characterization of Gompeertz–Verhulst distribution. J. Stat. Theory Appl. 13(1), 17–26 (2013)

    Google Scholar 

  4. Ahuja, J.C.: On certain properties of the generalized Gompertz distribution. Indian J. Stat. Ser. B 31, 541–544 (1969)

    Google Scholar 

  5. Ahuja, J.C., Nash, S.W.: The generalized Gompertz–Verhulst family of distributions. Sankhya Ser. A 29, 141–156 (1967)

    MathSciNet  MATH  Google Scholar 

  6. Amblard, C., Girard, S.: Symmetry and dependence properties within a semiparametric family of bivariate copulas. J. Nonparametric Stat. 14(6), 715–727 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Arnold, B.C., Balakrishnan, N., Nagaraja, H.N.: Records, Wiley Series in Probability and Statistics: Probability and Statistics. Wiley, New York (1998)

    Google Scholar 

  8. Bairamov, I., Kotz, S.: Dependence structure and symmetry of Huang–Kotz FGM distributions and their extensions. Metrika 56(1), 55–72 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  9. Barakat, H.M., El-Shandidy, M.A.: Computing the distribution and expected value of the concomitant rank order statistics. Commun. Stat. Theory Meth. 33(11), 2575–2594 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Barakat, H.M., Nigm, E.M., Harpy, M.H.: Limit theorems of order statistics and record values from the gamma and Kumaraswamy-generated-distributions. Bull. Malays. Math. Sci. (2016). doi:10.1007/s40840-016-0356-9

    Article  MATH  Google Scholar 

  11. Bdair, O.M., Raqab, M.Z.: Mean residual life of kth records under double monitoring. Bull. Malays. Math. Sci. Soc. 37(2), 457–464 (2014)

    MathSciNet  MATH  Google Scholar 

  12. Beg, M.I., Ahsanullah, M.: Concomitants of generalized order statistics from Farlie–Gumbel–Morgenstern distributions. Stat. Methodol. 5, 1–20 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Bhattacharya, P.K.: Convergence of sample paths of normalized sums of induced order statistics. Ann. Stat. 2, 1034–1039 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  14. Chen, Z., Bai, Z., Sinha, B.K.: Ranked Set Sampling: Theory and Applications. Springer, New York (2004)

    Book  MATH  Google Scholar 

  15. David, H.A.: Concomitants of order statistics. Bull. Int. Stat. Inst. 45, 295–300 (1973)

    MathSciNet  Google Scholar 

  16. David, H.A., Nagaraja, H.N.: Concomitants of order statistics. In: Balakrishnan, N., Rao, C.R. (eds.) Order Statistics: Theory & Methods, pp. 487–513. Elsevier, Amsterdam (1998)

    MATH  Google Scholar 

  17. David, H.A., Nagaraja, H.N.: Order Statistics, 3rd edn. Wiley, New York (2003)

    Book  MATH  Google Scholar 

  18. David, H.A., O’Connell, M.J., Yang, S.S.: Distribution and expected value of the rank of a concomitant and an order statistic. Ann. Stat. 5, 216–223 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  19. Fischer, M., Klein, I.: Constructing generalized FGM copulas by means of certain univariate distributions. Metrika 65(243), 260 (2007)

    MathSciNet  MATH  Google Scholar 

  20. Galambos, J.: The Asymptotic Theory of Extreme Order Statistics, 2nd edn. Krieger, Malabar (1987)

    MATH  Google Scholar 

  21. Gompertz, B.: On the nature of the function expressive of the human mortality and on a new mode of determining the value of life contingencies. Philos. Transduct. R. Soc. Lond. 115, 513–585 (1825)

    Article  Google Scholar 

  22. Gupta, R.D., Kundu, D.: Generalized exponential distributions. Aust. N. Z. J. Stat. 41, 173–188 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  23. Houchens, R.L.: Record Value Theory and Inference. ProQuest LLC, Ann Arbor (1984)

    Google Scholar 

  24. Huang, J.S., Kotz, S.: Modifications of the Farlie–Gumbel–Morgenstern distributions. A tough hill to climb. Metrika 49, 135–145 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  25. Mokhlis, N.A., Khames, S.K.: Concomitants of record values from a general Farlie–Gumbel–Morgenstern distributoion. J. Adv. Math. 7(3), 1328–1340 (2014a)

    Google Scholar 

  26. Mokhlis, N.A., Khames, S.K.: On concomitants of record values from generalized Farlie–Gumbel–Morgenstern distributoion. J. Stat. Sci. Appl. 2, 175–192 (2014b)

    Google Scholar 

  27. Tahmasebi, S., Behboodian, J.: Shannon information for concomitants of generalized order statistics in Farlie–Gumbel–Morgenstern (FGM) family. Bull. Malays. Math. Sci. Soc. 35(4), 975–981 (2012)

    MathSciNet  MATH  Google Scholar 

  28. Tahmasebi, S., Jafari, A.A.: Estimators for the parameter mean of Morgenstern type bivariate generalized exponential distribution using ranked set sampling. SORT 38(2), 161–180 (2014)

    MathSciNet  MATH  Google Scholar 

  29. Tahmasebi, S., Jafari, A.A.: Concomitants of order statistics and record values from Morgenstern type bivariate-generalized exponential distribution. Bull. Malays. Math. Sci. Soc. 38, 1411–1423 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  30. Tahmasebi, S., Jafari, A.A., Afshari, M.: Concomitants of dual generalized order statistics from Morgenstern type bivariate generalized exponential distribution. J. Stat. Theory Appl. 14(1), 1–12 (2015)

    Article  MathSciNet  Google Scholar 

  31. Tahmasebi, S., Jafari, A.A., Ahsanullah, M.: Properties on concomitants of generalized order statistics from a bivariate Rayleigh distribution. Bull. Malays. Math. Sci. Soc (2016). doi:10.1007/s40840-015-0297-8

    Article  MATH  Google Scholar 

  32. Verhulstt, P.F.: Notice sur la loi la population suit dans son accroissement. Correspondence mathematique et physique publiee L. A. J. Quetelet 10, 112–121 (1838)

    Google Scholar 

  33. Verhulst, P.F.: Recherches matheatiques sur la loi d’accorissement de la population. Nouvelles Mem. Ser. (2J) 18, 38 (1845)

    Google Scholar 

  34. Verhulst, P.F.: Deuxieme memoire sur la loi d’accorissement de la population. Memoires de L’Academie Royale des Sciences des Lettres et des beaux-Arts de Belgique Ser. 2 20, 32 (1847)

    Google Scholar 

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Acknowledgements

The authors are grateful to the Editor in Chief, Professor Rosihan M. Ali, and the anonymous referees for suggestions and comments that improved the presentation substantially.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

    H. M. Barakat & E. M. Nigm

  2. Higher Technological Institute, 10th of Ramadan city, Egypt

    A. H. Syam

Authors
  1. H. M. Barakat
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  2. E. M. Nigm
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  3. A. H. Syam
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Correspondence to H. M. Barakat.

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Barakat, H.M., Nigm, E.M. & Syam, A.H. Concomitants of Ordered Variables from Huang–Kotz FGM Type Bivariate Generalized Exponential Distribution. Bull. Malays. Math. Sci. Soc. 42, 337–353 (2019). https://doi.org/10.1007/s40840-017-0489-5

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  • DOI: https://doi.org/10.1007/s40840-017-0489-5

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