Amir Hamzeh KHAMMAR, Seyyed Mahdi AMİR JAHANSHAHİ, Hassan ZAREİ

On quantile-based dynamic survival extropy and its applications

The cumulative residual extropy is an uncertainty measure that parallels extropy in an absolutely continuous cumulative distribution function. The dynamic version of this measure is known as dynamic survival extropy. In this paper, we study some properties of the dynamic survival extropy using quantile function approach. Unlike the dynamic survival extropy, the quantile-based dynamic survival extropy determines the quantile density function uniquely through a simple relationship. We also extend the definition of quantile-based dynamic survival extropy into order statistics. Finally, an application of new quantile-based uncertainty measure as a risk measure is derived.

Keywords:

Characterization, dynamic survival extropy, quantile function, reliability measures, order statistics risk measure, stochastic orders, uncertainty,

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[1] S. Baratpour and A.H. Khammar, A quantile-based generalized dynamic cumulative measure of entropy, Commun. Stat. Theory Methods 47, 3104-3117, 2017.
[2] A. Di Crescenzo, B. Martinucci and J. Mulero, A quantile-based probabilistic mean value theorem, Probab Eng Inf Sci 30, 261-280, 2016.
[3] W. Gilchrist, Statistical Modelling with Quantile Functions, Boca Raton, FL: Chapman and Hall/CRC, 2000.
[4] T. Gneiting and A.E. Raftery, Strictly proper scoring rules, prediction, and estimation, J Am Stat Assoc 102, 359-378, 2007.
[5] S.M.A. Jahanshahi, H. Zarei and A.H. Khammar, On cumulative residual extropy, Probab Eng Inf Sci 34 (4), 605-625, 2020.
[6] J. Jose and E.I.A. Sathar, Extropy for past life Based on classical records, J. Indian Soc. Probab. Stat. 22, 27-46, 2021.
[7] J. Jose and E.I.A. Sathar, Residual extropy of k-record values, Stat Probab Lett 146, 1-6, 2019.
[8] A.H. Khammar and S.M.A. Jahanshahi, Quantile based Tsallis entropy in residual lifetime, Physica A 492, 994-1006, 2018.
[9] 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 49, 457-474, 2020.
[10] S. Krishnan, S.M. Sunoj and P.G. Sankaran, Some reliability properties of extropy and its related measures using quantile function, Statistica 80, 413-437, 2021.
[11] V. Kumar and Rekha, A quantile approach of Tsallis entropy for order statistics, Physica A 503, 916-928, 2018.
[12] F. Lad, G. Sanfilippo and G. Agro, Extropy: Complementary dual of entropy, Stat Sci 30, 40-58, 2015.
[13] N.N. Midhu, P.G. Sankaran and N.U. Nair, A class of distributions with the linear mean residual quantile function and its generalizations, Stat Methodol 15, 1-24, 2013.
[14] N.U. Nair, P.G. Sankaran and N. Balakrishnan, Quantile-Based Reliability Analysis. New York: Springer, 2013.
[15] N.U. Nair and B. Vineshkumar, Relation between cumulative residual entropy and excess wealth transform with applications to reliability and risk, Stoch. Qual. Control 36 (1), 43-57, 2021.
[16] A.K. Nanda, P.G. Sankaran and S.M. Sunoj, Renyi’s residual entropy: A quantile approach, Stat Probab Lett 85, 114-121, 2017.
[17] H.A. Noughabi and J. Jarrahiferiz, Extropy of order statistics applied to testing symmetry, Commun. Stat. Simul. Comput. 51 (6), 3389-3399, 2022.
[18] G. Psarrakos and A. Toomaj, On the generalized cumulative residual entropy with applications in actuarial science, J. Comput. Appl. Math. 309, 186-199, 2017.
[19] G. Qiu and A. Eftekharian, Extropy information of maximum and minimum ranked set sampling with unequal samples, Commun. Stat. Theory Methods Doi:10.1080/03610926.2019.1678640, 2020.
[20] G. Qiu and K. Jia, The residual extropy of order statistics, Stat Probab Lett 133, 15-22, 2018.
[21] G. Qiu, L. Wang and X. Wang, On extropy properties of mixed systems, Probab Eng Inf Sci 33, 471-86, 2019.
[22] M.Z. Raqab and G. Qiu, On extropy properties of ranked set sampling, Statistics 53, 210-26, 2019.
[23] P.G. Sankaran and S.M. Sunoj, Quantile based cumulative entropies, Commun. Stat. Theory Methods 46, 805-814, 2017.
[24] E.I.A. Sathar and J. Jose, Extropy based on records for random variables representing residual life, Commun. Stat. Simul. Comput. 52 (1), 196-206, 2020.
[25] E.L.A. Sathar and R.D. Nair, On the dynamic survival extropy, Commun. Stat. Theory Methods 50 (6), 1295-1313, 2021.
[26] M. Shaked and J.G. Shanthikumar, Stochastic Orders. Springer, New York, 2007.
[27] C.E. Shannon, A mathematical theory of communication, Bell Syst. tech. j. 27, 379- 423, 1948.
[28] S.M. Sunoj, A.S. Krishnan and P.G. Sankaran, Quantile based entropy of order statistics, J. Indian Soc. Probab. Stat. 18, 1-17, 2017.
[29] S.M. Sunoj and P.G. Sankaran, Quantile based entropy function, Stat Probab Lett 82, 1049-1053, 2017.
[30] S.M. Sunoj, P.G. Sankaran and N.U. Nair, Quantile-based cumulative Kullback-Leibler divergence, Statistics 52, 1-17, 2018.
[31] B. Vineshkumar, N.U Nair and P.G. Sankaran, Stochastic orders using quantile-based reliability functions, J Korean Stat Soc 44, 221-231, 2015.
[32] S. Wang, An actuarial index of the right-tail risk, N Am Actuar J 2, 88-101, 1998.
[33] V. Yang, Study on cumulative residual entropy and variance as risk measure, in: 5th International conference on business intelligence and financial engineering, published in IEEE 4, 2012.
[34] J. Yang, W. Xia and T. Hu, Bounds on extropy with variational distance constraint, Probab Eng Inf Sci 33, 186-204, 2019.