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Fisher information in order statistics and their concomitants for Cambanis bivariate distribution

  • Islam A. Husseiny , Haroon M. Barakat , Taher S. Taher EMAIL logo and Metwally A. Alawady
Published/Copyright: May 24, 2024
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Abstract

The Fisher information matrix (FIM) relevant to order statistics (OSs) and their concomitants of the shape-parameters vector of the Cambanis bivariate distribution is investigated. Singly or multiply censored bivariate samples drawn from the Cambanis bivariate distribution are used to obtain the Fisher information (FI). In addition, the FI contained in the scale and shape parameters of generalized exponential distributions in the concomitants of OSs is obtained. The cumulative residual FI in the concomitant of OSs based on the Cambanis family is theoretically and numerically studied. Finally, a bivariate real-world data set has been analyzed for illustrative purposes, and the performance of the proposed method is quite satisfactory.

MSC 2010: 62B10; 62G30

Acknowledgement

The authors are grateful to the anonymous reviewers for their careful and diligent reading, which improves the readability and presentation substantially.

  1. Communicated by Gejza Wimmer

References

[1] Abd Elgawad, M. A.—Alawady, M. A.: On concomitants of generalized order statistics from generalized FGM family under a general setting, Math. Slovaca 72(2) (2022), 507–526.10.1515/ms-2022-0033Search in Google Scholar

[2] Abd Elgawad, M. A.—Alawady, M. A.—Barakat, H. M.—Xiong, S.: Concomitants of generalized order statistics from Huang–Kotz Farlie–Gumbel–Morgenstern bivariate distribution: some information measures, Bull. Malays. Math. Sci. Soc. 43(3) (2020), 2627–2645.10.1007/s40840-019-00822-9Search in Google Scholar

[3] Abd Elgawad, M. A.—Barakat, H. M.—Alawady, M. A.: Concomitants of generalized order statistics under the generalization of Farlie–Gumbel–Morgenstern type bivariate distributions, Bull. Iranian Math. Soc. 47(4) (2021), 1045–1068.10.1007/s41980-020-00427-0Search in Google Scholar

[4] Abd Elgawad, M. A.—Barakat, H. M.—Alawady, M. A.: Concomitants of generalized order statistics from bivariate Cambanis family: Some information measures, Bull. Iranian. Math. Soc. 48(2) (2021), 563–585.10.1007/s41980-021-00532-8Search in Google Scholar

[5] Abd Elgawad, M. A.—Barakat, H. M.—Xiong, S.—Alyami, S. A.: Information measures for generalized order statistics and their concomitants under general framework from Huang–Kotz FGM bivariate distribution, Entropy 23(3) (2021), Art. No. 335.10.3390/e23030335Search in Google Scholar PubMed PubMed Central

[6] Abo-Eleneen, Z. A.—Nagaraja, H. N.: Fisher information in an order statistic and its concomitant, Ann. Inst. Statist. Math. 54(3) (2002), 667–680.10.1023/A:1022479514859Search in Google Scholar

[7] Abo-Eleneen, Z. A.—Nagaraja, H. N.: Fisher information in order statistics and their concomitants in bivariate censored samples, Metrika 67(3) (2008), 327–347.10.1007/s00184-007-0136-5Search in Google Scholar

[8] Ahmed, D.—Khames, S.—Mokhlis, N. A.: Inference for stress-strength models based on the bivariate general Farlie–Gumbel–Morgenstern distributions, J. Stat. Appl. Prob. Lett. 7(3) (2020), 141–150.10.18576/jsapl/070304Search in Google Scholar

[9] Alawady, M. A.—Barakat, H. M.—Xiong, S.—Abd Elgawad, M. A.: Concomitants of generalized order statistics from iterated Farlie–Gumbel–Morgenstern type bivariate distribution, Comm. Statist. Theory Methods 51(16) (2020), 5488–5504.10.1080/03610926.2020.1842452Search in Google Scholar

[10] Alawady, M. A.—Barakat, H. M.—Xiong, S.—Abd Elgawad, M. A.: On concomitants of dual generalized order statistics from Bairamov–Kotz–Becki Farlie–Gumbel–Morgenstern bivariate distributions, Asian-Eur. J. Math. 14(10) (2021), Art. ID 2150185.10.1142/S1793557121501850Search in Google Scholar

[11] Alawady, M. A.—Barakat, H. M.—Abd Elgawad, M. A.: Concomitants of generalized order statistics from bivariate Cambanis family of distributions under a general setting, Bull. Malays. Math. Sci. Soc. 44(5) (2021), 3129–3159.10.1007/s40840-021-01102-1Search in Google Scholar

[12] Al turk, L. I.—Abd Elaal, M. K.—Jarwan, R. S.: Inference of bivariate generalized exponential distribution based on copula functions, Appl. Math. Sci. 11(24) (2017), 1155–1186.10.12988/ams.2017.7398Search in Google Scholar

[13] Balasubramanian, K.—Balakrishnan, N.: On a class of multivariate distributions closed under concomitance of order statistics, Stat. Probab. Lett. 23 (1995), 239–242.10.1016/0167-7152(94)00119-SSearch in Google Scholar

[14] Barakat, H. M.—Nigm, E. M.—Alawady, M. A.—Husseiny, I. A.: Concomitants of order statistics and record values from generalization of FGM bivariate–generalized exponential distribution, J. Stat. Theory Appl. 18(3) (2019), 309–322.10.2991/jsta.d.190822.001Search in Google Scholar

[15] Barakat, H. M.—Nigm, E. M.—Husseiny, I. A.: Measures of information in order statistics and their concomitants for the single iterated Farlie–Gumbel–Morgenstern bivariate distribution, Math. Popul. Stud. 28(3) (2020), 154–175.10.1080/08898480.2020.1767926Search in Google Scholar

[16] 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(1) (2019), 337–353.10.1007/s40840-017-0489-5Search in Google Scholar

[17] Barakat, H. M.—Nigm, E. M.—Alawady, M. A.—Husseiny, I. A.: Concomitants of order statistics and record values from iterated FGM type bivariate-generalized exponential distribution, REVSTAT 19(2) (2020), 291–307.Search in Google Scholar

[18] Barakat, H. M.—Alawady, M. A.—Mansour, G. M.—Husseiny, I. A.: Sarmanov bivariate distribution: dependence structure-Fisher information in order statistics and their concomitants, Ric. Mat. (2022), 1–22.10.1007/s11587-022-00731-3Search in Google Scholar

[19] Barakat, H. M.—Alawady, M. A.—Husseiny, I. A.—Mansour, G. M.: Sarmanov family of bivariate distributions: statistical properties–concomitants of order statistics information measures, Bull. Malays. Math. Sci. Soc. 45(Suppl. 1) (2022), 49–83.10.1007/s40840-022-01241-zSearch in Google Scholar

[20] Bhattacharya, P. K.: Convergence of sample paths of normalized sums of induced order statistics, Ann. Statist. 2(5) (1974), 1034–1039.10.1214/aos/1176342823Search in Google Scholar

[21] Burkschat, M.—Cramer, E.: Fisher information in generalized order statistics, Statistics 46(6) (2012), 719–743.10.1080/02331888.2011.553802Search in Google Scholar

[22] Cambanis, S.: Some properties and generalizations of multivariate Eyraud–Gumbel–Morgenstern distributions, J. Multivariate Anal. 7(4) (1977), 551–559.10.1016/0047-259X(77)90066-5Search in Google Scholar

[23] David, H. A.: Concomitants of order statistics, Bull. Int. Statist. Inst. 45 (1973), 295–300.Search in Google Scholar

[24] Huang, J. S.—Kotz, S.: Correlation structure in iterated Farlie–Gumbel–Morgenstern distributions, Biometrika 71(3) (1984), 633–636.10.1093/biomet/71.3.633Search in Google Scholar

[25] Husseiny, I. A.—Syam, A. H.: The extropy of concomitants of generalized order statistics from Huang–Kotz–Morgenstern bivariate distribution, J. Math. 2022 (2022), Art. ID 6385998.10.1155/2022/6385998Search in Google Scholar

[26] Husseiny, I. A.—Alawady, M. A.—Barakat, H. M.—Abd Elgawad, M. A.: Information measures for order statistics and their concomitants from Cambanis bivariate family, Comm. Statist. Theory Methods 53(3) (2022), 865–881.10.1080/03610926.2022.2093909Search in Google Scholar

[27] Husseiny, I. A.—Barakat, H. M.—Mansour, G. M.—Alawady, M. A.: Information measures in records and their concomitants arising from Sarmanov family of bivariate distributions, J. Comput. Appl. Math. 408 (2022), 114–120.10.1016/j.cam.2022.114120Search in Google Scholar

[28] Kharazmi, O.—Balakrishnan, N.: Cumulative residual and Relativ cumulative residual Fisher information and their properties, IEEE Trans. Inform. Theory 67(10) (2021), 6306–6312.10.1109/TIT.2021.3073789Search in Google Scholar

[29] Koshti, R. D.—Kamalja, K. K.: Parameter estimation of Cambanis–type bivariate uniform distribution with ranked set sampling, J. Appl. Stat. 48(1) (2021), 61–83.10.1080/02664763.2019.1709808Search in Google Scholar PubMed PubMed Central

[30] Lad, F.—Sanfilippo, G.—Agro, G.: Extropy: complementary dual of entropy, Statist. Sci. 30 (2015), 40–58.10.1214/14-STS430Search in Google Scholar

[31] McGilchrist, C. A.—Aisbett, C. W.: Regression with frailty in survival analysis, Biometrics 47 (1991), 461–466.10.2307/2532138Search in Google Scholar

[32] Nair, N. U.—Scaria, J.—Mohan, S.: The Cambanis family of bivariate distributions: Properties and applications, Statistica 76(2) (2016), 169–184.Search in Google Scholar

[33] Nelsen, R. B.: An Introduction to Copulas, Springer, 2006.Search in Google Scholar

[34] Rao, C. R.: Linear Statistical Inference and its Applications, 2nd ed., Wiley New York, 1973.10.1002/9780470316436Search in Google Scholar

[35] Scaria, J.—Nair, N. U.: On concomitants of order statistics from Morgenstern Family, Biometrical J. 41(4) (1999), 483–489.10.1002/(SICI)1521-4036(199907)41:4<483::AID-BIMJ483>3.0.CO;2-2Search in Google Scholar

[36] 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(4) (2015), 1411–1423.10.1007/s40840-014-0087-8Search in Google Scholar

Received: 2023-02-24
Accepted: 2023-06-29
Published Online: 2024-05-24
Published in Print: 2024-04-25

© 2024 Mathematical Institute Slovak Academy of Sciences

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