Exploring Relationships and Inference Methods for Moments of Dual Generalized Order Statistics Derived from the Siddiqui-Dwivedi Distribution
Main Article Content
Abstract
In this paper, recurrence relation for single and product moments of dual generalized order statistics (DGOS) from Siddiqui-Dwivedi (SD) distribution are obtained. Furthermore, we provide the minimum variance linear unbiased estimator (MVLUE) of the position and scale parameters of the kth lower record values (LVR) and order statistics (OS) for the distribution under consideration. In the section 4, a characterization result is presented.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
References
Ahsanullah. M. A characterization of the uniform distribution by dual generalized order statistics. Comm. Statist.Theory Methods ,, 33, 2921–2928 (2004). https://doi.org/10.1081/STA-200038854
Athar,H., Anwar, Z. and Khan, R.U. On recurrence relations for the expectations of functions of lower generalized order statistics. Pak. J. Statist., 24(2), 111–122 (2008).
Athar, H. and Faizan, M. Moments of lower generalized order statistics from power function distribution and its characterization. International Journal of Statistical Sciences, 11 (Special Issue), 125–134 (2011).
Athar, H., Nayabuddin and Ali, M.A. Concomitants of Dual Generalized Order Statistics from Farlie Gumbel Morgenstern Type Bivariate Gumbel Distribution. IJSS, 14, 17–28 (2014). https://doi.org/10.1016/j.stamet.2007.04.001
Athar, H., Nayabuddin and M. Almech Ali. Concomitants of Dual Generalized Order Statistics from Bivariate Burr II Distribution. The South Pacific Journal of Natural and Applied Sciences, 33(1,2), 18–24 (2015a). doi: 10.1071/SP15004
Athar, H., Nayabuddin and Akhter, Z. Concomitants of Dual Generalized Order Statistics from Bivariate Burr III Distribution. Journal of Statistical Theory and Applications, 14(3), 240–256 (2015b). https://doi.org/10.2991/jsta.2015.14.3.2
Athar, H., Yousef F. Alh roi and Fawzy, M.A. A Study on Moments of Dual Generalized Order Statistics from Lxponentiated generalized Class of Distributions. Pak.j. st. t.oper. res, 17(3), 531–544 (2021). https://doi.org/10.18187/pjsor.v17i3.3338
Burkschat, M., Cramer, E. and Kamps, U. Dual generalized order statistics.METRON LXI, 13-26 (2003). https://doi.org/10.2991/978-94-6239-225-0_5
David, H.A., Nagaraja H.N. Order Statistics, John Wiley, New York (2003).
Dwivedi, S., Siddiqui, S. A., Dwivedi, P. and Siddiqui, I. Study of a Power Function As a Failure Model : Its Statistical and Mathematical Properties. Bulletin of Mathematics and Statistics Research, 7 (2), 26–35 (2019). http://dx.doi.org/10.33329/bomsr.72.26
Gupta N, Anwar Z. Relations for single and product moments of odd generalized exponential-Pareto distribution and characterization. Stat Optim Inf Comput., 7(1), 160–170 (2019). https://doi.org/10.19139/SOIC.V7I1.478
Khan, M.I. Moments of Dual Generalized Order Statistics from Generalized Inverted Kumaraswamy Distribution and Characterization. Thailand Statistician, 19(1), 140–153 (2021). https://doi.org/10.2991/JSTA.D.210219.001
Khatoon, B., Khan, M.J.S. and Noor, Z. Moments of Dual Generalized Order Statistics from Inverted Kumaraswamy Distribution and Related Inference. Journal of Statistical Theory and Applications, 20(2), 251–266 (2021). https://doi.org/10.2991/jsta.d.210219.001
Kumara,D., Nassarb,M., Deyd, S. and Elshahhate, A. Inferences for generalized Topp-Leone distribution under dual generalized order statistics with applications to Engineering and COVID-19 data. Model Assisted Statistics and Applications, 16, 125–141 (2021). http://dx.doi.org/10.3233/MAS-210525
Llyod,E.H. Least squares estimation of location and scale parameter using order statistics, Biometrika, 39, 88-95 (1952). https://doi.org/10.1093/BIOMET%2F39.1-2.88
Mbah, A. K. and Ahsanullah. M. Some characterization of the power function distribution based on lower generalized order statistics. Pak. J. Statist., 23, 139–146 (2007).
Nayabuddin. Concomitants of Dual Generalized Order Statistics from Farlie Gumbel Morgenstern Type Bivariate Power Function Distribution. Journal of Global Research in Mathematical Archives, 1(8), 79–90 (2013).
Nayabuddin and Salam, A. Ratio and inverse Moments of Concomitants of Dual Generalized Order Statistics from Farlie Gumbel Morgenstern Type Bivariate Inverse Weibull Distribution. Journal of Global Research in Mathematical Archives, 4(2), 16–19 (2017).
Pawlas, P. and Szynal, D. Recurrence relations for single and product moments of lower generalized order statistics from the inverse Weibull distribution. Demonstratio Math., XXXIV, 353–358 (2001). http://dx.doi.org/10.1515/dema-2001-0214