Research article

On concomitants of generalized order statistics arising from bivariate generalized Weibull distribution and its application in estimation

  • Received: 22 March 2024 Revised: 30 June 2024 Accepted: 08 July 2024 Published: 12 July 2024
  • MSC : 62G30, 62E15, 62H12

  • In this research, we studied the concomitants of generalized order statistics from the bivariate generalized Weibull distribution. We derived probability density functions and moments of concomitants of generalized order statistics from the bivariate generalized Weibull distribution. Moreover, utilizing the ranked set sample obtained from this distribution, we computed the best linear unbiased (BLU) estimator of the parameter connected with the study variable (variable of primary interest). Also, a real data application was presented.

    Citation: Areej M. AL-Zaydi. On concomitants of generalized order statistics arising from bivariate generalized Weibull distribution and its application in estimation[J]. AIMS Mathematics, 2024, 9(8): 22002-22021. doi: 10.3934/math.20241069

    Related Papers:

  • In this research, we studied the concomitants of generalized order statistics from the bivariate generalized Weibull distribution. We derived probability density functions and moments of concomitants of generalized order statistics from the bivariate generalized Weibull distribution. Moreover, utilizing the ranked set sample obtained from this distribution, we computed the best linear unbiased (BLU) estimator of the parameter connected with the study variable (variable of primary interest). Also, a real data application was presented.



    加载中


    [1] M. Ahsanullah, V. B. Nevzorov, Ordered random variables, Nova Science Publishers Incorporated (NY), 2001.
    [2] M. A. Alawady, H. M. Barakat, S. Xiong, M. A. Abd Elgawad, Concomitants of generalized order statistics from iterated Farlie–Gumbel–Morgenstern type bivariate distribution, Comm. Statist.-Theory Methods, 51 (2022), 5488–5504. https://doi.org/10.1080/03610926.2020.1842452 doi: 10.1080/03610926.2020.1842452
    [3] H. M. Barakat, E. M. Nigm, M. A. Alawady, I. A. Husseiny, Concomitants of order statistics and record values from iterated FGM type bivariate-generalized exponential distribution, REVSTAT-Statist. J., 19 (2021), 291–307. https://doi.org/10.57805/revstat.v19i2.344 doi: 10.57805/revstat.v19i2.344
    [4] M. I. Beg, M. Ahsanullah, Concomitants of generalized order statistics from Farlie-Gumbel-Morgenstern distributions, Stat. Methodol., 5 (2008), 1–20. https://doi.org/10.1016/j.stamet.2007.04.001 doi: 10.1016/j.stamet.2007.04.001
    [5] M. Chacko, P. Y. Thomas, Estimation of a parameter of Morgenstern type bivariate exponential distribution by ranked set sampling, Ann. Inst. Statist. Math., 60 (2008), 301–318. https://doi.org/10.1007/s10463-006-0088-y doi: 10.1007/s10463-006-0088-y
    [6] E. Chaumette, F. Vincent, Concomitant of ordered multivariate normal distribution with application to parametric inference, 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, 2017, 4481–4485. https://doi.org/10.1109/ICASSP.2017.7953004
    [7] Z. Chen, Z. Bai, B. K. Sinha, Ranked set sampling: theory and applications, Vol. 176, New York: Springer, 2004. https://doi.org/10.1007/978-0-387-21664-5
    [8] H. A. David, Concomitants of order statistics, Bull. Int. Statist. Inst., 45 (1973), 295–300.
    [9] H. A. David, H. N. Nagaraja, 18 Concomitants of order statistics, Handbook statist., 16 (1998), 487–513. https://doi.org/10.1016/S0169-7161(98)16020-0 doi: 10.1016/S0169-7161(98)16020-0
    [10] H. A. David, H. N. Nagaraja, Order statistics, John Wiley & Sons, 2004. https://doi.org/10.1002/0471722162
    [11] F. Domma, S. Giordano, Concomitants of m–generalized order statistics from generalized Farlie–Gumbel–Morgenstern distribution family, J. Comput. Appl. Math., 294 (2016), 413–435. https://doi.org/10.1016/j.cam.2015.08.022 doi: 10.1016/j.cam.2015.08.022
    [12] Y. F. Dong, W. X. Chen, M. Y. Xie, Best linear unbiased estimators of location and scale ranked set parameters under moving extremes sampling design, Acta Math. Appl. Sin., Engl. Ser., 39 (2023), 222–231. https://doi.org/10.1007/s10255-023-1043-x doi: 10.1007/s10255-023-1043-x
    [13] M. M. El-Din, M. M. Amein, M. S. Mohamed, Concomitants of case-Ⅱ of generalized order statistics from Farlie–Gumbel–Morgenstern distributions, J. Statist. Appl. Probabil., 3 (2014), 345. https://digitalcommons.aaru.edu.jo/jsap/vol3/iss3/5
    [14] I. S. Gradshteyn, I. M. Ryzhik, Table of integrals, series, and products, Academic press, 2014.
    [15] S. Hanif, M. Q. Shahbaz, Concomitants of generalized order statistics for a bivariate exponential distribution, Pak. J. Stat. Oper. Res., 12 (2016), 227–234. https://doi.org/10.18187/pjsor.v12i2.1326 doi: 10.18187/pjsor.v12i2.1326
    [16] M. R. Irshad, R. Maya, A. I. Al-Omari, S. P. Arun, G. Alomani, The extended Farlie–Gumbel–Morgenstern bivariate Lindley distribution: concomitants of order statistics and estimation, Electron. J. Appl. Stat. Anal., 14 (2021), 373–388. https://doi.org/10.1285/i20705948v14n2p373 doi: 10.1285/i20705948v14n2p373
    [17] M. R. Irshad, R. Maya, A. I. Al-Omari, A. A. Hanandeh, S. P. Arun, Estimation of a parameter of farlie-gumbel-morgenstern bivariate bilal distribution by ranked set sampling, Reliabil.: Theory Appl., 18 (2023), 164–175.
    [18] A. Jamalizadeh, N. Balakrishnan, Concomitants of order statistics from multivariate elliptical distributions, J. Stat. Plan. Infer., 142 (2012), 397–409. https://doi.org/10.1016/j.jspi.2011.07.010 doi: 10.1016/j.jspi.2011.07.010
    [19] A. Jamalizadeh, D. Kundu, Weighted Marshall–Olkin bivariate exponential distribution, Statistics, 47 (2013), 917–928. https://doi.org/10.1080/02331888.2012.670640 doi: 10.1080/02331888.2012.670640
    [20] M. Kamal, I. Alam, A. Rahman, A. Salam, S. Zarrin, Moments properties of concomitants of generalized order statistics from FGMTBM exponential distribution, Reliabil.: Theory Appl., 18 (2023), 348–358.
    [21] K. K. Kamalja, R. D. Koshti, Application of ranked set sampling in parameter estimation of cambanis-type bivariate exponential distribution, Statistica, 82 (2022), 145–175. https://doi.org/10.6092/issn.1973-2201/11973 doi: 10.6092/issn.1973-2201/11973
    [22] U. Kamps, A concept of generalized order statistics, J. Stat. Plan. Infer., 48 (1995), 1–23. https://doi.org/10.1016/0378-3758(94)00147-N doi: 10.1016/0378-3758(94)00147-N
    [23] U. Kamps, E. Cramer, On distributions of generalized order statistics, Statistics, 35 (2007), 269–280. https://doi.org/10.1080/02331880108802736 doi: 10.1080/02331880108802736
    [24] A. H. Khan, M. J. S. Khan, On ratio and inverse moment of generalized order statistics from Burr distribution, Pak. J. Stat., 28 (2012), 59–68.
    [25] T. Kollo, Multivariate skewness and kurtosis measures with an application in ICA, J. Multivariate Anal., 99 (2008), 2328–2338. https://doi.org/10.1016/j.jmva.2008.02.033 doi: 10.1016/j.jmva.2008.02.033
    [26] R. D. Koshti, K. K. Kamalja, Parameter estimation of Cambanis-type bivariate uniform distribution with ranked set sampling, J. Appl. Stat., 48 (2021), 61–83. https://doi.org/10.1080/02664763.2019.1709808 doi: 10.1080/02664763.2019.1709808
    [27] R. D. Koshti, K. K. Kamalja, Efficient estimation of a scale parameter of bivariate Lomax distribution by ranked set sampling, Calcutta Statist. Assoc. Bull., 73 (2021), 24–44. https://doi.org/10.1177/0008068321992520 doi: 10.1177/0008068321992520
    [28] R. D. Koshti, K. K. Kamalja, A review on concomitants of order statistics and its application in parameter estimation under ranked set sampling, J. Korean Stat. Soc., 53 (2024), 65–99. https://doi.org/10.1007/s42952-023-00235-2 doi: 10.1007/s42952-023-00235-2
    [29] S. Kumar, M. J. S. Khan, S. Kumar, Concomitant of order statistics from new bivariate gompertz distribution, J. Mod. Appl. Stat. Meth., 18 (2019), 1–20. https://doi.org/10.56801/10.56801/v18.i.1056 doi: 10.56801/10.56801/v18.i.1056
    [30] A. M. Mathai, R. K. Saxena, Generalized hypergeometric functions with applications in statistics and physical sciences, Vol. 348, Springer Berlin, Heidelberg, 1973. https://doi.org/10.1007/BFb0060468
    [31] G. A. McIntyre, A method for unbiased selective sampling, using ranked sets, Aust. J. Agr. Res., 3 (1952), 385–390. https://doi.org/10.1071/AR9520385 doi: 10.1071/AR9520385
    [32] S. M. Mirhosseini, M. Amini, D. Kundu, A. Dolati, On a new absolutely continuous bivariate generalized exponential distribution, Stat. Methods Appl., 24 (2015), 61–83. https://doi.org/10.1007/s10260-014-0276-5 doi: 10.1007/s10260-014-0276-5
    [33] L. Muraleedharan, M. Chacko, Interval prediction of order statistics and record values using concomitants of order statistics and record values for Morgenstern family of distributions, J. Stat. Res., 56 (2023), 55–73. https://doi.org/10.3329/jsr.v56i1.63946 doi: 10.3329/jsr.v56i1.63946
    [34] A. K. Pathak, M. Arshad, Q. J. Azhad, M. Khetan, A. Pandey, A novel bivariate generalized Weibull distribution with properties and applications, Amer. J. Math. Management Sci., 42 (2023), 279–306. https://doi.org/10.1080/01966324.2023.2239963 doi: 10.1080/01966324.2023.2239963
    [35] A. K. Pathak, P. Vellaisamy, A bivariate generalized linear exponential distribution: properties and estimation, Commun. Stat.-Simul. Comput., 51 (2022), 5426–5446. https://doi.org/10.1080/03610918.2020.1771591 doi: 10.1080/03610918.2020.1771591
    [36] A. Philip, P. Y. Thomas, On concomitants of order statistics arising from the extended Farlie$-$Gumbel$-$Morgenstern bivariate logistic distribution and its application in estimation, Stat. Methodol., 25 (2015), 59–73. https://doi.org/10.1016/j.stamet.2015.02.002 doi: 10.1016/j.stamet.2015.02.002
    [37] A. Philip, P. Y. Thomas, On concomitants of order statistics and its application in defining ranked set sampling from Farlie–Gumbel–Morgenstern bivariate Lomax distribution, JIRSS, 16 (2017), 67–95.
    [38] A. Philip, P. Y. Thomas, On concomitants of order statistics from Farlie$-$Gumbel$-$Morgenstern bivariate lomax distribution and its application in estimation, JIRSS, 16 (2022), 67–95.
    [39] S. H. Shahbaz, M. Al-Sobhi, M. Q. Shahbaz, B. Al-Zahrani, A new multivariate Weibull distribution. Pak. J. Stat. Oper. Res., 14 (2018), 75–88. https://doi.org/10.18187/pjsor.v14i1.2192 doi: 10.18187/pjsor.v14i1.2192
    [40] S. H. Shahbaz, M. Q. Shahbaz, Concomitants of generalized order statistics for a bivariate Weibull distribution, Pak. J. Stat. Oper. Res., 13 (2017), 867–874. https://doi.org/10.18187/pjsor.v13i4.2139 doi: 10.18187/pjsor.v13i4.2139
    [41] A. Sheikhi, Y. Mehrali, M. Tata, On the exact joint distribution of a linear combination of order statistics and their concomitants in an exchangeable multivariate normal distribution, Stat. Papers, 54 (2013), 325–332. https://doi.org/10.1007/s00362-012-0430-9 doi: 10.1007/s00362-012-0430-9
    [42] S. L. Stokes, Ranked set sampling with concomitant variables, Comm. Statist.-Theory Methods, 6 (1977), 1207–1211. https://doi.org/10.1080/03610927708827563 doi: 10.1080/03610927708827563
    [43] S. L. Stokes, Inferences on the correlation coefficient in bivariate normal populations from ranked set samples, J. Amer. Statist. Assoc., 75 (1980), 989–995. https://doi.org/10.1080/01621459.1980.10477584 doi: 10.1080/01621459.1980.10477584
    [44] S. Tahmasebi, A. A. Jafari, M. Ahsanullah, Properties on concomitants of generalized order statistics from a bivariate Rayleigh distribution, Bull. Malays. Math. Sci. Soc., 41 (2018), 355–370. https://doi.org/10.1007/s40840-015-0297-8 doi: 10.1007/s40840-015-0297-8
    [45] K. Takahasi, K. Wakimoto, On unbiased estimates of the population mean based on the sample stratified by means of ordering, Ann. Inst. Stat. Math., 20 (1968), 1–31. https://doi.org/10.1007/BF02911622 doi: 10.1007/BF02911622
    [46] T. G. Veena, P. Y. Thomas, Role of concomitants of order statistics in determining parent bivariate distributions, Comm. Statist.-Theory Methods, 46 (2017), 7976–7997. https://doi.org/10.1080/03610926.2016.1171351 doi: 10.1080/03610926.2016.1171351
    [47] S. S. Yang, General distribution theory of the concomitants of order statistics, Ann. Statist., 5 (1977), 996–1002. https://doi.org/10.1214/aos/1176343954 doi: 10.1214/aos/1176343954
  • Reader Comments
  • © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(108) PDF downloads(26) Cited by(0)

Article outline

Figures and Tables

Tables(11)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog