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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 und Metwally A. Alawady
Veröffentlicht/Copyright: 24. Mai 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-2022-0033Suche 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/s40840-019-00822-9Suche 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/s41980-020-00427-0Suche 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/s41980-021-00532-8Suche 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/e23030335Suche 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:1022479514859Suche 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/s00184-007-0136-5Suche 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/070304Suche 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), 5488–5504.10.1080/03610926.2020.1842452Suche 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/S1793557121501850Suche 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/s40840-021-01102-1Suche 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.2017.7398Suche 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-SSuche 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.190822.001Suche 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), 154–175.10.1080/08898480.2020.1767926Suche 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/s40840-017-0489-5Suche 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.Suche 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/s11587-022-00731-3Suche 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-zSuche 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/1176342823Suche in Google Scholar

[21] Burkschat, M.—Cramer, E.: Fisher information in generalized order statistics, Statistics 46(6) (2012), 719–743.10.1080/02331888.2011.553802Suche 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)90066-5Suche in Google Scholar

[23] David, H. A.: Concomitants of order statistics, Bull. Int. Statist. Inst. 45 (1973), 295–300.Suche 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/71.3.633Suche 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 6385998.10.1155/2022/6385998Suche 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), 865–881.10.1080/03610926.2022.2093909Suche 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.2022.114120Suche 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.2021.3073789Suche 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), 61–83.10.1080/02664763.2019.1709808Suche 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-STS430Suche in Google Scholar

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

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

[34] Rao, C. R.: Linear Statistical Inference and its Applications, 2nd ed., Wiley New York, 1973.10.1002/9780470316436Suche 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;2-2Suche 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/s40840-014-0087-8Suche 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

Heruntergeladen am 26.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2024-0038/html
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