Abstract
The main focus of this article is on the study of properties and characterizations of dynamic survival extropy and its scaled version. Its relation with other well-known measures is also discussed. A simple nonparametric estimator and a nonparametric estimator based on the kernel are proposed for survival extropy and scaled dynamic survival extropy respectively. These estimators could also be utilized to estimate the measures related to dynamic survival extropy, such as the Gini index. In addition, the performance of the suggested estimators is evaluated for the simulated data set.
Acknowledgements
The authors would like to thank the editor and the reviewer for their valuable comments, which have considerably improved the earlier version of the article.
References
[1] M. C. Bhattacharjee, How rich are the rich? Modeling affluence and inequality via reliability theory, Sankhyā Ser. B 55 (1993), no. 1, 1–26. Suche in Google Scholar
[2] M. Chandra and N. D. Singpurwalla, Relationships between some notions which are common to reliability theory and economics, Math. Oper. Res. 6 (1981), no. 1, 113–121. 10.1287/moor.6.1.113Suche in Google Scholar
[3] C. Gini, Variabilita e Mutabilita, Tipografia di Paolo Cuppini, Bologna, 1912. Suche in Google Scholar
[4] R. C. Gupta, Role of equilibrium distribution in reliability studies, Probab. Engrg. Inform. Sci. 21 (2007), no. 2, 315–334. 10.1017/S0269964807070192Suche in Google Scholar
[5] S. M. A. Jahanshahi, H. Zarei and A. H. Khammar, On cumulative residual extropy, Probab. Engrg. Inform. Sci. 34 (2020), no. 4, 605–625. 10.1017/S0269964819000196Suche in Google Scholar
[6] J. Jose and E. I. Abdul Sathar, Residual extropy of 𝑘-record values, Statist. Probab. Lett. 146 (2019), 1–6. 10.1016/j.spl.2018.10.019Suche in Google Scholar
[7] O. Kamari and F. Buono, On extropy of past lifetime distribution, Ric. Mat. 70 (2021), no. 2, 505–515. 10.1007/s11587-020-00488-7Suche in Google Scholar
[8] A. S. Krishnan, S. M. Sunoj and N. Unnikrishnan Nair, Some reliability properties of extropy for residual and past lifetime random variables, J. Korean Statist. Soc. 49 (2020), no. 2, 457–474. 10.1007/s42952-019-00023-xSuche in Google Scholar
[9] C. Kundu, On cumulative residual (past) extropy of extreme order statistics, preprint (2020), https://arxiv.org/abs/2004.12787. 10.1080/03610926.2021.2021238Suche in Google Scholar
[10] F. Lad, G. Sanfilippo and G. Agrò, Extropy: Complementary dual of entropy, Statist. Sci. 30 (2015), no. 1, 40–58. 10.1214/14-STS430Suche in Google Scholar
[11] F. Lad, G. Sanfilippo and G. Agrò, The duality of entropy/extropy, and completion of the Kullback information complex, Entropy 20 (2018), Paper No. 593. 10.3390/e20080593Suche in Google Scholar PubMed PubMed Central
[12] S. P. Mukherjee and D. Roy, Some characterizations of the exponential and related life distributions, Calcutta Stat. Assoc. Bull. 35 (1986), 189–197. 10.1177/0008068319860308Suche in Google Scholar
[13] R. D. Nair and E. I. A. Sathar, On dynamic failure extropy, J. Indian Soc. Probab. Statist. 21 (2020), no. 2, 287–313. 10.1007/s41096-020-00083-xSuche in Google Scholar
[14] H. A. Noughabi and J. Jarrahiferiz, On the estimation of extropy, J. Nonparametr. Stat. 31 (2019), no. 1, 88–99. 10.1080/10485252.2018.1533133Suche in Google Scholar
[15] E. Parzen, On estimation of a probability density function and mode, Ann. Math. Statist. 33 (1962), no. 3, 1065–1076. 10.1214/aoms/1177704472Suche in Google Scholar
[16] G. Qiu and K. Jia, The residual extropy of order statistics, Statist. Probab. Lett. 133 (2018), 15–22. 10.1016/j.spl.2017.09.014Suche in Google Scholar
[17] E. I. A. Sathar and R. D. Nair, On dynamic survival extropy, Comm. Statist. Theory Methods 50 (2021), no. 6, 1295–1313. 10.1080/03610926.2019.1649426Suche in Google Scholar
[18] E. I. A. Sathar and R. D. Nair, On dynamic weighted extropy, J. Comput. Appl. Math. 393 (2021), Paper No. 113507. 10.1016/j.cam.2021.113507Suche in Google Scholar
[19] M. Shaked and J. G. Shanthikumar, Stochastic Orders and Their Applications, Probab. Math. Statist., Academic Press, Boston, 1994. Suche in Google Scholar
[20] C. E. Shannon, A mathematical theory of communication, Bell System Tech. J. 27 (1948), 379–423, 623–656. 10.1002/j.1538-7305.1948.tb01338.xSuche in Google Scholar
[21] S. Tahmasebi and A. Toomaj, On negative cumulative extropy with applications, Comm. Statist. Theory Methods (2020), 10.1080/03610926.2020.1831541. 10.1080/03610926.2020.1831541Suche in Google Scholar
© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On Generalized Reflected BSDEs with Rcll Obstacle
- Estimations of Means and Variances in a Markov Linear Model
- Impact of Financial Crisis on Economic Growth: A Stochastic Model
- A Study on Some Properties of Dynamic Survival Extropy and Its Relation to Economic Measures
- Test for Decreasing Mean Residual Lifetimes Based on the Cumulative Residual Renyi’s Entropy
- Multiple Dependent State Sampling Inspection Plan for Lindley Distributed Quality Characteristic
- The SPRT Sign Chart for Process Dispersion
Artikel in diesem Heft
- Frontmatter
- On Generalized Reflected BSDEs with Rcll Obstacle
- Estimations of Means and Variances in a Markov Linear Model
- Impact of Financial Crisis on Economic Growth: A Stochastic Model
- A Study on Some Properties of Dynamic Survival Extropy and Its Relation to Economic Measures
- Test for Decreasing Mean Residual Lifetimes Based on the Cumulative Residual Renyi’s Entropy
- Multiple Dependent State Sampling Inspection Plan for Lindley Distributed Quality Characteristic
- The SPRT Sign Chart for Process Dispersion