Weighted extensions of generalized cumulative residual entropy and their applications

References

• Asadi, M., and Y. Zohrevand. 2007. On the dynamic cumulative residual entropy. Journal of Statistical Planning and Inference 137 (6):1931–41. doi: 10.1016/j.jspi.2006.06.035.
   Web of Science ®Google Scholar
• Baxter, L. A. 1982. Reliability applications of the relevation transform. Naval Research Logistics Quarterly 29 (2):323–30. doi: 10.1002/nav.3800290212.
   Google Scholar
• Bdair, O. M., and M. Z. Raqab. 2012. Sharp upper bounds for the mean residual waiting time of records. Statistics 46 (1):69–84. doi: 10.1080/02331888.2010.498044.
   Web of Science ®Google Scholar
• Di Crescenzo, A. 1999. A probabilistic analogue of the mean value theorem and its applications to reliability theory. Journal of Applied Probability 36 (3):706–19. doi: 10.1239/jap/1029349973.
   Web of Science ®Google Scholar
• Di Crescenzo, A., and A. Toomaj. 2017. Furher results on the generalized cunulative entropy. Kybernetika 53 (5):959–82.
   Web of Science ®Google Scholar
• Di Crescenzo, A., and M. Longobardi. 2006. On weighted residual and past entropies. Scientiae Mathematicae Japonicae 64:255–66.
   Google Scholar
• Di Crescenzo, A., and M. Longobardi. 2009. On cumulative entropies. Journal of Statistical Planning and Inference 139 (12):4072–87. doi: 10.1016/j.jspi.2009.05.038.
   Web of Science ®Google Scholar
• Dziubdziela, W., and B. Kopocinski. 1976. Limiting properties of the k-th record value. Applicationes Mathematicae 15:187–90. doi: 10.4064/am-15-2-187-190.
   Google Scholar
• Gupta, R. C., and R. D. Gupta. 2007. Proportional reversed hazard rate model and its applications. Journal of Statistical Planning and Inference 137 (11):3525–36. doi: 10.1016/j.jspi.2007.03.029.
   Web of Science ®Google Scholar
• Kapodistria, S., and G. Psarrakos. 2012. Some extensions of the residual lifetime and its connection to the cumulative residual entropy. Probability in the Engineering and Informational Sciences 26 (1):129–46. doi: 10.1017/S0269964811000271.
   Web of Science ®Google Scholar
• Kayal, S. 2016. On generalized cumulative entropies. Probability in the Engineering and Informational Sciences 30 (4):640–62. doi: 10.1017/S0269964816000218.
   Web of Science ®Google Scholar
• Kayal, S. 2018. On weighted generalized cumulative residual entropy of order n. Methodology and Computing in Applied Probability 20 (2):487–503. doi: 10.1007/s11009-017-9569-0.
   Web of Science ®Google Scholar
• Klein, I., B. Mangold, and M. Doll. 2016. Cumulative paired φ-entropy. Entropy 18 (7):248–5. doi: 10.3390/e18070248.
   Web of Science ®Google Scholar
• Krakowski, M. 1973. The relevation transform and a generalization of the Gamma distribution function. Revue Française D’automatique, Informatique, Recherche Opérationnelle. Recherche Opérationnelle 7 (2):107–20. doi: 10.1051/ro/197307V201071.
   Google Scholar
• Mirali, M., and S. Baratpour. 2017a. Dynamic version of weighted cumulative residual entropy. Communications in Statistics-Theory and Methods 46 (22):11047–59. doi: 10.1080/03610926.2016.1257711.
   Web of Science ®Google Scholar
• Mirali, M., and S. Baratpour. 2017b. Some results on weighted cumulative entropy. Journal of the Iranian Statistical Society 17 (2):21–32.
   Google Scholar
• Mirali, M., S. Baratpour, and V. Fakoor. 2017. On weighted cumulative residual entropy. Communications in Statistics - Theory and Methods 46 (6):2857–69. doi: 10.1080/03610926.2015.1053932.
   Web of Science ®Google Scholar
• Misagh, F., Y. Panahi, G. H. Yari, and R. Shahi. 2011. Weighted cumulative entropy and its estimation. IEEE International Conference on Quality and Reliability (ICQR): Bangkok, Thailand, 477–80.
   Google Scholar
• Navarro, J., Y. del Aguila, and M. Asadi. 2010. Some new results on the cumulative residual entropy. Journal of Statistical Planning and Inference 140 (1):310–22. doi: 10.1016/j.jspi.2009.07.015.
   Web of Science ®Google Scholar
• Psarrakos, G., and J. Navarro. 2013. Generalized cumulative residual entropy and record values. Metrika 76 (5):623–40. doi: 10.1007/s00184-012-0408-6.
   Web of Science ®Google Scholar
• Pyke, R. 1965. Spacings. Journal of Royal Statistical Society 27:395–449. doi: 10.1111/j.2517-6161.1965.tb00602.x.
   Google Scholar
• Rao, M., Y. Chen, B. C. Vemuri, and F. Wang. 2004. Cumulative residual entropy: A new measure of information. IEEE Transactions on Information Theory 50 (6):1220–8. doi: 10.1109/TIT.2004.828057.
   Web of Science ®Google Scholar
• Raqab, M. Z., and M. Asadi. 2010. Some results on the mean residual waiting time of records. Statistics 44 (5):493–504. doi: 10.1080/02331880903189158.
   Web of Science ®Google Scholar
• Shaked, M., and J. G. Shanthikumar. 2007. Stochastic orders. New York: Springer.
   Google Scholar
• Shannon, C. 1948. A mathematical theory of communication. Bell System Technical Journal 27 (3):379–432. doi: 10.1002/j.1538-7305.1948.tb01338.x.
   Google Scholar
• Smith, R. L., and J. C. Naylor. 1987. A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Applied Statistics 36 (3):358–69. doi: 10.2307/2347795.
   Web of Science ®Google Scholar
• Suhov, Y., and S. Yasaei Sekeh. 2015. Weighted cumulative entropies: An extention of CRE and CE. arXiv: 1507.07051v1. [cs.IT].
   Google Scholar
• Sunoj, S. M., and M. N. Linu. 2012. Dynamic cumulative residual Renyis entropy. Statistics 46 (1):41–56. doi: 10.1080/02331888.2010.494730.
   Web of Science ®Google Scholar