Past Extropy of π-Records
-
E. I. Abdul Sathar
and
Jitto Jose
Abstract
Recently, A.βS. Krishnan, S.βM. Sunoj and N.βU. Nair [Some reliability properties of extropy for residual and past lifetime random variables, J. Korean Stat. Soc. 2020, 10.1007/s42952-019-00023-x] introduced past extropy for measuring uncertainty contained in past lifetime of random variables. In the present study, we focus on the past extropy of k-records. The motivation for considering past extropy of k-records has been discussed in detail. We have also illustrated the merit of considering past extropy of k-records over past extropy of classical records and past extropy of original random sample using two real life data sets. Some important properties of past extropy of k-records are discussed in this work. We have expressed past extropy of k-records using past extropy of k-records arising from uniform distribution. The work proposes a simple estimator for past extropy of k-records as well.
Acknowledgements
The authors express their sincere gratitude to the editor-in-chief and the referee for their valuable and constructive comments that helped to improve the earlier version of the article to a great extent.
References
[1] M. Ahsanullah, Record values, random record models and concomitants, J. Statist. Res. 28 (1994), no. 1β2, 89β109. Search in Google Scholar
[2] B. C. Arnold, N. Balakrishnan and H. N. Nagaraja, Records, Wiley Ser. Probab. Stat. Probab. Stat., John Wiley & Sons, New York, 1998. 10.1002/9781118150412Search in Google Scholar
[3] R. U. Ayres and K. MartinΓ s, Waste potential entropy: The ultimate ecotoxic, Econ. Appl. 48 (1995), 95β120. Search in Google Scholar
[4] D. Cox and E. Snell, Applied Statistics-Principles and Examples. , Vol. 2, CRC Press, Boca Raton, 1981. 10.1007/978-94-009-5838-8Search in Google Scholar
[5] H. A. David and H. N. Nagaraja, Order statistics, 3rd ed., Wiley Series in Probability and Statistics, Wiley-Interscience, Hoboken, 2003. 10.1002/0471722162Search in Google Scholar
[6] A. Di Crescenzo and M. Longobardi, Entropy-based measure of uncertainty in past lifetime distributions, J. Appl. Probab. 39 (2002), no. 2, 434β440. 10.1017/S002190020002266XSearch in Google Scholar
[7] W. Dziubdziela and B. KopociΕski, Limiting properties of the k-th record values, Zastos. Mat. 15 (1976), no. 2, 187β190. 10.4064/am-15-2-187-190Search in Google Scholar
[8] R. Goel, H. C. Taneja and V. Kumar, Measure of entropy for past lifetime and k-record statistics, Phys. A 503 (2018), 623β631. 10.1016/j.physa.2018.02.200Search in Google Scholar
[9] R. C. Gupta and S. N. U. A. Kirmani, On the proportional mean residual life model and its implications, Statistics 32 (1998), no. 2, 175β187. 10.1080/02331889808802660Search in Google Scholar
[10] R. C. Gupta and S. N. U. A. Kirmani, Characterization based on convex conditional mean function, J. Statist. Plann. Inference 138 (2008), no. 4, 964β970. 10.1016/j.jspi.2007.03.059Search in Google Scholar
[11] G. Hofmann and N. Balakrishnan, Fisher information in k-records, Ann. Inst. Statist. Math. 56 (2004), no. 2, 383β396. 10.1007/BF02530552Search in Google Scholar
[12] A. S. Krishnan, S. M. Sunoj and N. U. Nair, Some reliability properties of extropy for residual and past lifetime random variables, J. Korean Stat. Soc. (2020), 10.1007/s42952-019-00023-x. 10.1007/s42952-019-00023-xSearch in Google Scholar
[13] J. Jose and E. I. Abdul Sathar, Residual extropy of k-record values, Statist. Probab. Lett. 146 (2019), 1β6. 10.1016/j.spl.2018.10.019Search in Google Scholar
[14] F. Lad, G. Sanfilippo and G. AgrΓ², Extropy: Complementary dual of entropy, Statist. Sci. 30 (2015), no. 1, 40β58. 10.1214/14-STS430Search in Google Scholar
[15] M. Madadi and M. Tata, Shannon information in k-records, Comm. Statist. Theory Methods 43 (2014), no. 15, 3286β3301. 10.1080/03610926.2012.697965Search in Google Scholar
[16] K. Martinas and M. Frankowicz, Extropy-reformulation of the entropy principle, Period. Polytechn. Chem. Eng. 44 (2000), no. 1, 29β38. Search in Google Scholar
[17] V. B. Nevzorov, Records: Mathematical Theory, Transl. Math. Monogr. 194, American Mathematical Society, Providence, 2001. 10.1090/mmono/194Search in Google Scholar
[18] J.-Z. Pan and Z.-X. Lu, Relationship between paddy soil adhesion to steel and to rubber, J. Terramech. 35 (1998), no. 3, 155β158. 10.1016/S0022-4898(98)00019-6Search in Google Scholar
[19] C. E. Shannon, A mathematical theory of communication, Bell System Tech. J. 27 (1948), no. 3, 379β423, 623β656. 10.1002/j.1538-7305.1948.tb01338.xSearch in Google Scholar
[20] S. Tahmasebi and M. Eskandarzadeh, Generalized cumulative entropy based on kth lower record values, Statist. Probab. Lett. 126 (2017), 164β172. 10.1016/j.spl.2017.02.036Search in Google Scholar
Β© 2020 Walter de Gruyter GmbH, Berlin/Boston
