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Nair, R. Dhanya; Sathar, E. I. Abdul

Some useful results related to various measures of extropy and their interrelationship. (English) Zbl 1524.62493

Stat. Probab. Lett. 193, Article ID 109729, 6 p. (2023).
Summary: This study concentrates on various extropy measures and their interrelationships. The relationship connecting L-moments and extropy measures was identified. We also discuss the association between extropy variants via equilibrium distribution. Relationships between various uncertainty measures are also provided.

Cited in 1 Document

MSC:

62N05 Reliability and life testing
62B10 Statistical aspects of information-theoretic topics
94A17 Measures of information, entropy

Keywords:

entropy; extropy; L-moments; equilibrium distribution

Software:

LMOMENTS
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Full Text: DOI

References:

[1] Abbasnejad, M.; Arghami, N. R.; Morgenthaler, S.; Mohtashami Borzadaran, G. R., On the dynamic survival entropy, Statist. Probab. Lett., 80, 1962-1971 (2010) · Zbl 1202.62002
[2] Asadi, M.; Zohrevand, Y., On the dynamic cumulative residual entropy, J. Statist. Plann. Inference, 137, 1931-1941 (2007) · Zbl 1118.62006
[3] Csiszar, I.; Shields, P., Information theory and statistics: A tutorial, Found. Trends Commun. Inform. Theory, 1, 4, 417-528 (2004) · Zbl 1156.62300
[4] Di Crescenzo, A.; Longobardi, M., Entropy-based measure of uncertainty in past lifetime distributions, J. Appl. Probab., 39, 2, 434-440 (2002) · Zbl 1003.62087
[5] Di Crescenzo, A.; Longobardi, M., On weighted residual and past entropies, Sci. Math. Jpn., 64, 255-266 (2006) · Zbl 1106.62114
[6] Di Crescenzo, A.; Longobardi, M., On cumulative entropies, J. Statist. Plann. Inference, 139, 4072-4087 (2009) · Zbl 1172.94543
[7] Ebrahimi, N., How to measure uncertainty in the residual lifetime distributions, Sankhya, 58, 48-56 (1996) · Zbl 0893.62098
[8] Greenwood, J. A.; Landwehr, J. M.; Matalas, N. C.; Wallis, J. R., Probability weighted moments: definitions and relation to parameters of several distributions expressed in inverse form, Water Resour. Res., 15, 6, 1049-1054 (1979)
[9] Gupta, R. C., Role of equilibrium distribution in reliability studies, Probab. Engrg. Inform. Sci., 21, 315-334 (2007) · Zbl 1115.60081
[10] Hosking, J. R.M., L-moments: Analysis and estimation of distributions using linear combination of order statistics, J. R. Stat. Soc., 52, 1, 105-124 (1990) · Zbl 0703.62018
[11] Jahanshahi, S. M.A.; Zarei, H.; Khammar, A. H., On cumulative residual extropy, Probab. Engrg. Inform. Sci., 34, 4, 605-625 (2020) · Zbl 1485.62007
[12] Krishnan, A. S.; Sunoj, S. M.; Nair, N. U., Some reliability properties of extropy for residual and past lifetime random variables, J. Korean Stat. Soc., 49, 457-474 (2020) · Zbl 1487.94063
[13] Lad, F.; Sanfilippo, G.; Agro, G., Extropy: Complementary dual of entropy, Statist. Sci., 30, 40-58 (2015) · Zbl 1332.62027
[14] Misagh, F., Panahi, Y., Yari, G.H., Shahi, R., 2011. Weighted cumulative entropy and its estimation. In: Proceedings of the IEEE International Conference on Quality and Reliability. ICQR, pp. 477-480.
[15] Nair, R. D.; Sathar, E. I.A., On dynamic failure extropy, J. Indian Soc. Probab. Stat., 21, 2, 287-313 (2020)
[16] Nair, R. D.; Sathar, E. I.A., A study on some properties of dynamic survival extropy and its relation to economic measures, Stoch. Qual. Control (2022) · Zbl 1498.94043
[17] Nair, N. U.; Vineshkumar, B., L-moments of residual life, J. Statist. Plann. Inference, 140, 2618-2631 (2010) · Zbl 1188.62293
[18] Qiu, G.; Jia, K., The residual extropy of order statistics, Statist. Probab. Lett., 133, 15-22 (2018) · Zbl 1440.62164
[19] Rao, M.; Chen, Y.; Vemuri, B. C.; Wang, F., Cumulative residual entropy: a new measure of information, IEEE Trans. Inform. Theory, 50, 1220-1228 (2004) · Zbl 1302.94025
[20] Sathar, E. I.A.; Nair, R. D., On dynamic survival extropy, Comm. Statist. Theory Methods, 50, 6, 1295-1313 (2021) · Zbl 07532949
[21] Sathar, E. I.A.; Nair, R. D., On dynamic weighted extropy, J. Comput. Appl. Math., 393 (2021) · Zbl 1464.62204
[22] Sathar, E. I.A.; Nair, R. D., A study on weighted dynamic survival and failure extropies, Comm. Statist. Theory Methods, 1-20 (2021)
[23] Shannon, C. E., A mathematical theory of communication, Bell Syst. Techn., 27 (1948), 379-423 and 623-656 · Zbl 1154.94303
[24] Tahmasebi, S.; Toomaj, A., On negative cumulative extropy with applications, Comm. Statist. Theory Methods (2020) · Zbl 07565476
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