Concomitants of lower record statistics for Bivariate Pseudo Powered Inverse Rayleigh distribution.
Main Article Content
Abstract
The concept of p- th record value was introduced by Dziubdziela and Kopocinski (1976). In this paper, we have considered concomitants of p- th lower record values (LRV) for Bivariate Pseudo Powered Inverse Rayleigh (BPPIR) distribution. Further single and joint distribution of concomitants of p- th LRV are obtained and expressions for single and product moments are derived. Additionally, we provide the minimum variance linear unbiased estimator of the location and scale parameters of the concomitants of p-th lower record values. The tables for survival function and hazard function has also been obtained. The explicit expression for the reliability is also derived for BPPIR distribution.
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
[1] Ahsanullah, M. Records and concomitants. Bull. Malays. Math., 32(2), 101–117 (2009).
[2] Ahsanullah, M. Concomitants of Upper Record Statistics for Bivariate Pseudo-Weibull Distribution. Applications and Applied Mathematics, 5(2), 282-291 (2010).
[3] Asgharzadeh, A. & Abdi, M. Confidence intervals for the parameters of the Burr type XII distribution based on Records. Int. Journ. Statist. and Econ., 8, 96-114 (2012).
[4] Barakat, H.M., Nigm, E.M. & Syam, A.H. Concomitants of order statistics and record values from Bairamov–Kotz–Bekci FGM bivariate-generalized exponential distribution. Filomat Journal, 32(9), 3313–3324 (2018). https://doi.org/10.2298/FIL1809313B
[5] 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 – Statistical Journal, 19(2), 291-307 (2021). https://doi.org/10.57805/revstat.v19i2.344
[6] Bdair, O.M. & Raqab, M.Z. Mean residual life of kth records under double monitoring. Bull. Malaysia Math. Soc. 37(2), 457–464 (2013).
[7] Chandler, K.M. The distribution and frequency of record values. J. Roy. Statist. Soc., Ser. B, 14, 220-228 (1952). https://doi.org/10.1111/j.2517-6161.1952.tb00115.x
[8] Dziubdziela, W. & Kopocionski, B. Limiting properties of the k-th record values . Appl. Math., 15(2), 187-190 (1976).
[9] Filus, J.K. & Filus, L.Z. On some Bivariate Pseudo normal densities. Pak. J. Statist.17(1), 1-19 (2001).
[10] Filus, J.K. & Filus, L.Z. On some new classes of Multivariate Probability Distributions. Pak. J. Statist. 22(1), 21–42, (2006).
[11] Gradshteyn, I.S. & Ryzhik, I.M. Table of Integral, Series and Product, 7th Edn., Academic Press, USA, (2007).
[12] Khan, M.A, & Khan, R.U. k−th upper record values from modified Weibull distribution and characterization. Int. J. Comp. Theo. Stat., 3, 75-80 (2016).
[13] Khan, R.U. & Zia, B. Recurrence relation for the moments of generalized inverse Weibull distribution based on lower records and a characterization. GSTF Journal of Mathematics, Statistics and Operations Research, 2, 68–71 (2013).
[14] Khan, M. J. S., Sharma, A., Khan, M.I. & Kumar, S. Exact Moments of Record Values from Burr Distribution with Applications. Int. J. Comp. Theo. Stat. 2(2), 107-115 (2015).
[15] Khan, R.U., Khan, M.A. & Khan, M.A.R. Relations for moments of generalized record values from additive Weibull distribution and associated inference. Stat. Optim. Inf. Comput.,5, 127-136 (2017). https://doi.org/10.19139/soic.v5i2.237
[16] Kumar, D. & Dey, S. Upper record values from extended exponential distribution. Journal of Modern Applied Statistical Methods, 17(2), eP2687 (2018). doi:10.22237/jmasm/1557149263
[17] Llyod, E.H. Least squares estimation of location and scale parameter using order statistics. Biometrika, 39, 88-95 (1952). https://doi.org/10.2307/2332466
[18] Minimol, S. & Thomas, P.Y. On some properties of Makeham distribution using generalized record values and its characterization. Braz. J. Probab. Stat., 27,487-501 (2013).https://doi.org/10.1214/11-BJPS178
[19] Minimol, S. & Thomas, P.Y. On characterization of Gompertz distribution by properties of generalized record values. J Stat Theory Appl., 13, 38-45 (2014). https://doi.org/10.2991/jsta.2014.13.1.4
[20] Mohsin, M., Ahmad, M., Shahbaz, S. & Shahbaz, M.Q. Concomitants of lower records for bivariate Pseudo-inverse Rayleigh distribution. Sci. Int. 21 (1), 21-23 (2009).
[21] Paul, J. & Thomas, P.Y. Concomitant record ranked set sampling. Comm. in Statist. – Theory and Meth., 46(19), 9518–9540 (2017).
[22] Pawlas, P. & Szynal, D. Relations for single and product moments of k-th record values from exponential and Gumbel distributions. J. Appl. Statist. Sci 7, 53-62 (1998).
[23] Shahbaz, S. H. & Ahmad, M. Concomitants of order statistics for Bivariate Pseudo–Weibull distribution. World App. Sci. J., 6 (10), 1409–1412 (2009).
[24] Shahbaz, M.Q., Shahbaz, S., Mohsin, M., & Rafiq, A. On distribution of bivariate concomitants of records. Applied Mathematics Letters, 23, 567-570 (2010). https://doi.org/10.1016/j.aml.2010.01.012
[25] Singh, B. & Khan, R. U. Moments of extended Erlang-truncated exponential distribution based on k-th lower record values and characterizations. Int. J. Math. Stat. Invent. 6, 65–74 (2018).
[26] Singh, B., Khan, R. U. & Zarrin, S. Moments of generalized upper record values from Weibull- power function distribution and characterization. J. Stat. Appl. Pro., 9(2), 309-318 (2020). http://dx.doi.org/10.18576/jsap/090211
[27] 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, 1411–1423 (2015). https://doi.org/10.1007/s40840-014-0087-8