An ordered approach on cumulative extropy measures for information analysis

References

• Abbasnejad, M. 2011. Some characterization results based on dynamic survival and failure entropies. Communications for Statistical Applications and Methods 18 (6):787–98. doi:10.5351/CKSS.2011.18.6.787.
   Google Scholar
• Ahmadi, J., and M. Fashandi. 2019. Characterization of symmetric distributions based on some information measures properties of order statistics. Physica A: Statistical Mechanics and Its Applications 517:141–52. doi:10.1016/j.physa.2018.11.009.
   Web of Science ®Google Scholar
• Aliprantis, C. D., and O. Burkinshaw. 1981. Principles of real analysis. North Holland: Elsevier.
   Google Scholar
• Arnold, B. C., N. Balakrishnan, and H. N. Nagaraja. 2008. A first course in order statistics. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
   Google Scholar
• Asha, G., and C. Rejeesh. 2015. Characterizations using past entropy measures. Metron 73 (1):119–34. doi:10.1007/s40300-014-0053-0.
   Web of Science ®Google Scholar
• Balakrishnan, N., and A. Selvitella. 2017. Symmetry of a distribution via symmetry of order statistics. Statistics & Probability Letters 129:367–72. doi:10.1016/j.spl.2017.06.023.
   Web of Science ®Google Scholar
• Baratpour, S. 2010. Characterizations based on cumulative residual entropy of first-order statistics. Communications in Statistics - Theory and Methods 39 (20):3645–51. doi:10.1080/03610920903324841.
   Web of Science ®Google Scholar
• Chechile, R. A. 2011. Properties of reverse hazard functions. Journal of Mathematical Psychology 55 (3):203–22. doi:10.1016/j.jmp.2011.03.001.
   Web of Science ®Google Scholar
• David, H. A., and H. N. Nagaraja. 2003. Order Statistics. New York: Wiley.
   Google Scholar
• Fashandi, M., and J. Ahmadi. 2012. Characterizations of symmetric distributions based on Rényi entropy. Statistics & Probability Letters 82 (4):798–804. doi:10.1016/j.spl.2012.01.004.
   Web of Science ®Google Scholar
• Higgins, J. R. 2004. Completeness and basis properties of sets of special functions. New York: Cambridge University Press.
   Google Scholar
• Hinkley, D. V. 1975. On power transformations to symmetry. Biometrika 62 (1):101–11. doi:10.1093/biomet/62.1.101.
   Web of Science ®Google Scholar
• Honerkamp, J. 2012. Statistical physics: An advanced approach with applications. New York: Springer Science & Business Media.
   Google Scholar
• Jahanshahi, S. M. A., H. Zarei, and A. H. Khammar. 2020. On cumulative residual extropy. Probability in the Engineering and Informational Sciences 34 (4):605–25. doi:10.1017/S0269964819000196.
   Web of Science ®Google Scholar
• Jose, J., and E. I. A. Sathar. 2019. Residual extropy of k-record values. Statistics & Probability Letters 146 (C):1–6. doi:10.1016/j.spl.2018.10.019.
   Web of Science ®Google Scholar
• Kamari, O. 2017. Characterizations based on cumulative entropy of the last-order statistics. International Journal of Statistics and Probability 6 (3):183. doi:10.5539/ijsp.v6n3p183.
   Google Scholar
• Lad, F., G. Sanfilippo, and G. Agro. 2015. Extropy: Complementary dual of entropy. Statistical Science 30 (1):40–58. doi:10.1214/14-STS430.
   Web of Science ®Google Scholar
• Qiu, G. 2017. The extropy of order statistics and record values. Statistics & Probability Letters 120:52–60. doi:10.1016/j.spl.2016.09.016.
   Web of Science ®Google Scholar
• Qiu, G., and K. Jia. 2018a. Extropy estimators with applications in testing uniformity. Journal of Nonparametric Statistics 30 (1):182–96. doi:10.1080/10485252.2017.1404063.
   Web of Science ®Google Scholar
• Qiu, G., and K. Jia. 2018b. The residual extropy of order statistics. Statistics & Probability Letters 133:15–22. doi:10.1016/j.spl.2017.09.014.
   Web of Science ®Google Scholar
• Sathar, E. I. A., and J. Jose. 2020a. Extropy based on records for random variables representing residual life. Communications in Statistics-Simulation and Computation. Advance online publication. doi:10.1080/03610918.2020.1851715.
   Google Scholar
• Sathar, E. I. A., and J. Jose. 2020b. Past extropy of k-records. Stochastics and Quality Control 35 (1):25–38. doi:10.1515/eqc-2019-0023.
   Google Scholar
• Sathar, E. I. A., and D. R. Nair. 2021. On dynamic survival extropy. Communications in Statistics - Theory and Methods 50 (6), 1295–313. doi:10.1080/03610926.2019.1649426.
   Web of Science ®Google Scholar
• Shannon, C. E. 1948. A mathematical theory of communication. Bell System Technical Journal 27 (3):379–423. doi:10.1002/j.1538-7305.1948.tb01338.x.
   Google Scholar
• Tahmasebi, S., and A. Toomaj. 2020. On negative cumulative extropy with applications. Communications in Statistics-Theory and Methods. Advance online publication. doi:10.1080/03610926.2020.1831541.
   Web of Science ®Google Scholar
• Thomas, P. Y., and J. Jose. 2020. A new bivariate distribution with Rayleigh and Lindley distributions as marginals. Journal of Statistical Theory and Practice 14 (2):28. doi:10.1007/s42519-020-00093-9.
   Web of Science ®Google Scholar
• Yang, L. 2012. Study on cumulative residual entropy and variance as risk measure. In Fifth International Conference on Business Intelligence and Financial Engineering, 210–3. IEEE.
   Google Scholar