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Farlie–Gumbel–Morgenstern Bivariate Moment Exponential Distribution and Its Inferences Based on Concomitants of Order Statistics

Author

Listed:
  • Sasikumar Padmini Arun

    (Kerala University Library, Research Centre, University of Kerala, Trivandrum 695 034, India)

  • Christophe Chesneau

    (Department of Mathematics, Université de Caen Basse-Normandie, 14032 Caen, France)

  • Radhakumari Maya

    (Department of Statistics, University College, Trivandrum 695 034, India)

  • Muhammed Rasheed Irshad

    (Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, India)

Abstract

In this research, we design the Farlie–Gumbel–Morgenstern bivariate moment exponential distribution, a bivariate analogue of the moment exponential distribution, using the Farlie–Gumbel–Morgenstern approach. With the analysis of real-life data, the competitiveness of the Farlie–Gumbel–Morgenstern bivariate moment exponential distribution in comparison with the other Farlie–Gumbel–Morgenstern distributions is discussed. Based on the Farlie–Gumbel–Morgenstern bivariate moment exponential distribution, we develop the distribution theory of concomitants of order statistics and derive the best linear unbiased estimator of the parameter associated with the variable of primary interest (study variable). Evaluations are also conducted regarding the efficiency comparison of the best linear unbiased estimator relative to the respective unbiased estimator. Additionally, empirical illustrations of the best linear unbiased estimator with respect to the unbiased estimator are performed.

Suggested Citation

  • Sasikumar Padmini Arun & Christophe Chesneau & Radhakumari Maya & Muhammed Rasheed Irshad, 2023. "Farlie–Gumbel–Morgenstern Bivariate Moment Exponential Distribution and Its Inferences Based on Concomitants of Order Statistics," Stats, MDPI, vol. 6(1), pages 1-15, February.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:1:p:15-267:d:1056541
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    References listed on IDEAS

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    1. Yogesh Mani Tripathi & Tanmay Kayal & Sanku Dey, 2017. "Estimation of the PDF and the CDF of exponentiated moment exponential distribution," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 1282-1296, November.
    2. Stuart G. Coles & Jonathan A. Tawn, 1994. "Statistical Methods for Multivariate Extremes: An Application to Structural Design," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(1), pages 1-31, March.
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