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  • 1 Persian Gulf University, Bushehr, Iran
  • 2 Yazd University, Yazd, Iran
  • 3 Rider University Lawrenceville, New Jersey 08648, U.S.A.
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The Rayleigh distribution is an important model in applications such as noise theory, height of the sea waves and wave length. In this paper, we first study the reliability characteristics of Morgenstern type bivariate Rayleigh distribution (MTBRD). Then, we investigate some properties on concomitants of order statistics and record values in MTBRD. Finally, we propose the best linear unbiased estimator for a parameter of MTBRD using both complete and censored samples based on concomitants of order statistics.

  • [1]

    Ahsanullah, M., Record statistics, Nova Science Publishers Commack, New York, 1995.

  • [2]

    Anderson, J. E., Louis, T. A., Holm, N. V. and Harvald, B., Time-dependent association measures for bivariate survival distributions, Journal of the American Statistical Association, 87(419) (1992) pp. 641650.

    • Search Google Scholar
    • Export Citation
  • [3]

    Arnold, B., Balakrishnan, N. and Nagaraja, H., Records, John Wiley & Sons Inc, New York, 1998.

  • [4]

    Bairamov, I. and Bekci, M., Concomitant of order statistics in FGM type bivariate uniform distributions, Istatistik, Journal of the Turkish Statistical Association, 2(2) (1999) pp. 135144.

    • Search Google Scholar
    • Export Citation
  • [5]

    Balasubramanian, K. and Beg, M. I., Concomitants of order statistics in Morgenstern type bivariate exponential distribution, Journal of Applied Statistical Science, 54(4) (1997) pp. 233245.

    • Search Google Scholar
    • Export Citation
  • [6]

    BuHamra, S. and Ahsanullah, M., On concomitants of bivariate Farlie-Gumbel- Morgenstern distributions, Pakistan Journal of Statistics, 29(4) (2013) pp. 453466.

    • Search Google Scholar
    • Export Citation
  • [7]

    Chacko, M. and Thomas, P. Y., Estimation of a parameter of Morgenstern type bivariate exponential distribution by ranked set sampling, Annals of the Institute of Statistical Mathematics, 60(2) (2008) pp. 301318.

    • Search Google Scholar
    • Export Citation
  • [8]

    Chacko, M. and Thomas, P. Y., Estimation of parameter of Morgenstern type bivariate exponential distribution using concomitants of order statistics, Statistical Methodology, 8(4) (2011) pp. 363376.

    • Search Google Scholar
    • Export Citation
  • [9]

    Clayton, D. G., A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence, Biometrika, 65(1) (1978) pp. 141151.

    • Search Google Scholar
    • Export Citation
  • [10]

    David, H. A. and Nagaraja, H., Order Statistics, John Wiley and Sons, 2003.

  • [11]

    D’Este, G., A Morgenstern-type bivariate gamma distribution, Biometrika, 68(1) (1981) pp. 339340.

  • [12]

    Gumbel, E. J., Bivariate exponential distributions, Journal of the American Statistical Association, 55(292) (1960) pp. 698707.

  • [13]

    Gumbel, E. J., Bivariate logistic distributions, Journal of the American Statistical Association, 56(294) (1961) pp. 335349.

  • [14]

    Gupta, R. C., Reliability characteristics of Farlie-Gumbel-Morgenstern family of bivariate distributions, Communications in Statistics-Theory and Methods, (2015) 10.1080/03610926. 2013.828075.

    • Search Google Scholar
    • Export Citation
  • [15]

    Houchens, R. L., Record value theory and inference, Dissertation Abstracts International Part B: Science and Engineering, 45(3) (1984).

    • Search Google Scholar
    • Export Citation
  • [16]

    Khaledi, B.-E. and Kochar, S., Stochastic comparisons and dependence among concomitants of order statistics, Journal of Multivariate Analysis, 73(2) (2000) pp. 262281.

    • Search Google Scholar
    • Export Citation
  • [17]

    Khames, S. and Mokhlis, N., Concomitants of record values from a general Farlie- Gumbel-Morgenstern distribution, Journal of Advances in Mathematics, 7(3) (2014) pp. 13171329.

    • Search Google Scholar
    • Export Citation
  • [18]

    Morgenstern, D., Einfache beispiele zweidimensionaler verteilungen, Mitteilingsblatt für Mathematishe Statistik, 8(1) (1956) pp. 234235.

    • Search Google Scholar
    • Export Citation
  • [19]

    Nevzorov, V. B. and Ahsanullah, M., Some distributions of induced records, Biometrical Journal, 42(8) (2000) pp. 10691081.

  • [20]

    Scaria, J. and Nair, N. U., On concomitants of order statistics from Morgenstern family, Biometrical Journal, 41(4) (1999) pp. 483489.

    • Search Google Scholar
    • Export Citation
  • [21]

    Shaked, M., A family of concepts of dependence for bivariate distributions, Journal of the American Statistical Association, 72(359) (1977) pp. 642650.

    • Search Google Scholar
    • Export Citation
  • [22]

    Shaked, M. and Shanthikumar, J. G., Stochastic Orders and Their Applications, Academic Press, San Diego, 1994.

  • [23]

    Tahmasebi, S. and Behboodian, J., A short note on entropy ordering property for concomitants of order statistics, World Applied Sciences Journal, 9(3) (2010) pp. 257258.

    • Search Google Scholar
    • Export Citation
  • [24]

    Tahmasebi, S. and Behboodian, J., Information properties for concomitants of order statistics in Farlie - Gumbel-Morgenstern (FGM) family, Communications in Statistics - Theory and Methods, 41(11) (2012) pp. 19541968.

    • Search Google Scholar
    • Export Citation
  • [25]

    Tahmasebi, S. and Jafari, A. A., Estimation of a scale parameter of Morgenstern type bivariate uniform distribution by ranked set sampling, Journal of Data Science, 10 (2012) pp. 129141.

    • Search Google Scholar
    • Export Citation
  • [26]

    Tahmasebi, S. and Jafari, A. A., Estimators for the parameter mean of Morgenstern type bivariate generalized exponential distribution using ranked set sampling, Statistics and Operations Research Transactions, 38(2) (2014) pp. 161180.

    • Search Google Scholar
    • Export Citation
  • [27]

    Tahmasebi, S. and Jafari, A. A., Concomitants of order statistics and record values from Morgenstern type bivariate generalized exponential distribution, Bulletin of the Malaysian Mathematical Sciences Society, 38(4) (2015) pp. 14111423.

    • Search Google Scholar
    • Export Citation
  • [28]

    Tahmasebi, S. and Jafari, A. A., A review on unbiased estimators of a parameter from morgenstern type bivariate gamma distribution using ranked set sampling, Azerbaijan Journal of Mathematics, 5(2) (2015) pp. 312.

    • Search Google Scholar
    • Export Citation