Results on concomitants of generalized order statistics from Morgenstern new family of heavy-tailed distributions

Document Type : Original Scientific Paper

Authors

1 Department of Statistics, Yazd University, Yazd, Iran

2 Department of Statistics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr, Iran

Abstract

In this paper‎, ‎a new bivariate family of distributions is proposed by mixing up the new family of heavy-tailed distributions approach with the Farlie-Gumble-Morgenstern copula‎. ‎The resultant family may be called the Farlie-Gumble-Morgenstern new family of heavy-tailed distributions‎. ‎For the proposed family‎, ‎some properties of the concomitants of generalized order statistics are obtained‎. ‎The joint distribution of concomitants is also derived‎. ‎Furthermore‎, ‎for this new family‎, ‎some properties of extropy for the concomitant of generalized order statistics are obtained‎. ‎The method of maximum likelihood estimation is implemented to obtain the estimators of the parameters‎. ‎Two sub-models are studied using the introduced approach.

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References

Abd Elgawad, M.A., Alawady, M.A., Barakat, H.M. and Xiong, S. (2020a). Concomitants of generalized order statistics from Huang-Kotz Farlie-Gumble-Morgenstern bivariate distribution: Some information measures. Bulletin of the Malaysian Mathematical Sciences Society, 43(3):2627–2645.
Abd Elgawad, M.A., Barakat, H.M. and Alawady, M.A. (2020b). Concomitants of generalized order statistics under the generalization of Farlie-Gumbel-Morgenstern-type bivariate distributions. Bulletin of the Iranian Mathematical Society, 47(4):1–24.
Ahmad, Z., Mahmoudi, E., Alizadeh, M., Roozegar, R. and Afify, A.Z. (2021). The exponential TX family of distributions: Properties and an Application to Insurance Data. Journal of Mathematics, 2021.
Alawady, M.A., Barakat, H.M., Xiong, S. and Abd Elgawad, M.A. (2020). Concomitants of generalized order statistics from iterated Farlie-Gumbel-Morgenstern type bivariate distribution. Communications in Statistics-Theory and Methods. https://doi.org/10.1080/03610926.2020.1842452.
AL-Hussaini, E.K. (2008). Generalized order statistics: prospective and applications. New Developments in Applied Statistics Research, 65.
Arnold, B., Balakrishnan, N. and Nagaraja, H. (1998). Records. New York: John Wiley & Sons Inc.
Beg, M.I. and Ahsanullah, M. (2008). Concomitants of generalized order statistics from Farlie-Gumbel-Morgenstern distributions. Statistical Methodology, 5(1):1–20.
Burkschat, M., Cramer, E. and Kamps, U. (2003). Dual generalized order statistics. Metron-International Journal of Statistics, 61(1):13–26.
EL-Sherpieny, E.A., Muhammed, H.Z. and Almetwally, E.M. (2018). FGM bivariate Weibull distribution. In Proceedings of the Annual Conference in Statistics (53rd), Computer Science, and Operations Research, Institute of Statistical Studies and Research, Cairo University.
Eryilmaz, S. (2005). Concomitants in a sequence of independent nonidentically distributed random vectors. Communications in Statistics-Theory and Methods, 34(9-10):1925–1933.
Farlie, D.G.J. (1960). The performance of some correlation coefficients for a general Bivariate distribution. Biometrika, 47(3/4):307–323.
Hanif, S. and Shahbaz, M.Q. (2016). Concomitants of generalized order statistics for a bivariate exponential distribution. Pakistan Journal of Statistics and Operation Research, XII(2):227–234.
Jafari, A.A., Almaspoor, Z. and Tahmasebi, S. (2021). General results on bivariate extended Weibull Morgenstern family and concomitants of its generalized order statistics. Ricerche di Matematica. https://doi.org/10.1007/s11587-021-00680-3.
Kamps, U. (1995). A concept of generalized order statistics. Journal of Statistical Planning and Inference, 48(1):1–23.
Kotb, M.S. (2017). On concomitants of ordered ranked set sampling from Morgenstern family. Journal of Mathematics and Statistics, 13(4):353–360.
Lad, F., Sanfilippo, G. and Agrò, G. (2015). Extropy: complementary dual of entropy. Statistical Science, 30(1):40–58.
Morgenstern, D. (1956). Einfache Beispiele zweidimensionaler Verteilungen. Mitt. Math. Stat, 8:234–235.
Pawlas, P. and Szynal, D. (2001). Recurrence relations for single and product moments of lower generalized order statistics from the inverse Weibull distribution. Demonstratio Mathematica, 34(2):141–146.
Scaria, J. and Nair, U. (1999). On concomitants of order statistics from Morgenstern family. Biometrical Journal: Journal of Mathematical Methods in Biosciences, 41(4):483–489.
Tahmasebi, S. and Jafari, A.A. (2012). Estimation of a scale parameter of Morgenstern type bivariate uniform distribution by ranked set sampling. Journal of Data Science, 10(1):129–141.
Tahmasebi, S. and Jafari, A.A. (2015a). Concomitants of order statistics and record values from Morgenstern type bivariate generalized exponential distribution. Bulletin of the Malaysian Mathematical Sciences Society, 38(4):1411–1423.
Tahmasebi, S. and Jafari, A.A. (2015c). A review on unbiased estimators of a parameter from Morgenstern type bivariate gamma distribution using ranked set sampling. Azerbaijan Journal of Mathematics, 5(2):3–12.
Tahmasebi, S., Jafari, A.A. and Afshari, M. (2015b). Concomitants of dual generalized order statistics from Morgenstern type bivariate generalized exponential distribution. Journal of Statistical Theory and Applications, 14(1):1–12.
Tahmasebi, S., Jafari, A.A. and Ahsanullah, M. (2018). Properties on concomitants of generalized order statistics from a bivariate Rayleigh distribution. Bulletin of the Malaysian Mathematical Sciences Society, 41(1):355–370.
Journal of Statistical Modelling: Theory and Applications
Volume 3, Issue 1
January 2022
Pages 9-24

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History

  • Receive Date: 27 May 2022
  • Revise Date: 10 August 2022
  • Accept Date: 17 August 2022

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