Abstract
The present paper considers a shift-dependent measure of uncertainty and its dynamic (residual) version. Various properties have been discussed. Two classes of lifetime distributions are proposed. Further, when m independent and identically distributed observations are available, an estimator of the measure under study is presented using empirical approach. In addition, large sample properties of the estimator are studied. Finally, an application of the proposed measure to the problem related to right-tail risk measure is presented.
Similar content being viewed by others
References
Abu-Youssef SE (2002) A moment inequality for decreasing (increasing) mean residual life distributions with hypothesis testing application. Statistics and Probability Letters 57:171–177
Arnold BC, Balakrishnan N, Nagaraja HN (1998) Records. Wiley, New York
Asadi M, Zohrevand Y (2007) On dynamic cumulative residual entropy. Journal of Statistical Planning and Inference 137:1931–1941
Billingsley P (1986) Probability and measure, 2nd Edn. Wiley, New York
Cover TM, Thomas JA (2006) Elements of information theory. Wiley, New York
Cox DR, Oakes D (2001) Analysis of survival data. Chapman and Hall
Di Crescenzo A, Longobardi M (2006) On weighted residual and past entropies. Scientiae Mathematicae Japonicae 64:255–266
Di Crescenzo A, Longobardi M (2009) On cumulative entropies. Journal of Statistical Planning and Inference 139:4072–4087
Kass RE, Ventura V, Cai C (2003) Statistical smooting of neural data. Netw Comput Neural Syst 14:5–15
Kayal S, Moharana R (2017) On weighted cumulative residual entropy. Journal of Statistics and Management Systems 20:153–173
Kayid M, Izadkhah S, Alhalees H (2016) Combination of mean residual life order with reliability applications. Statistical Methodology 29:51–69
Mirali M, Baratpour S, Fakoor V (2017) On weighted cumulative residual entropy. Communications in Statistics-Theory and Methods 46:2857–2869
Misagh F, Panahi Y, Yari GH, Shahi R (2011) Weighted Cumulative entropy and its estimation 2011 IEEE International Conference on Quality and Reliability (ICQR). doi:10.1109/ICQR.2011.6031765
Navarro J, Psarrakos G (2017) Characterizations based on generalized cumulative residual entropy functions. Communications in Statistics - Theory and Methods 46:1247–1260
Psarrakos G, Navarro J (2013) Generalized cumulative residual entropy and record values. Metrika 27:623–640
Psarrakos G, Toomaj A (2017) On the generalized cumulative residual entropy with applications in actuarial science. J Comput Appl Math 309:186–199
Pyke R (1965) Spacings. J R Stat Soc 27:395–449
Ramsay CM (1993) Loading gross premiums for risk without using utility theory. Transactions of the Society of Actuaries XLV
Rao M, Chen Y, Vernuri BC, Wang F (2004) Cumulative residual entropy: a new measure of information. IEEE Trans Inf Theory 50:1220–1228
Shaked M, Shanthikumar JG (2007) Stochastic orders. Springer Verlag, New York
Shannon C (1948) The mathematical theory of communication. Bell Syst Tech J 27:379–423
Wang S (1998) An actuarial index of the righ-tail risk. North American Actuarial Journal 2:88–101
Yang V (2012) Study on cumulative residual entropy and variance as risk measure 5th International conference on business intelligence and financial engineering, published in IEEE, p 4
Acknowledgments
The author would like to thank the Editor, Associate Editor and the two referees for careful reading and for their comments which greatly improved the article.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kayal, S. On Weighted Generalized Cumulative Residual Entropy of Order n . Methodol Comput Appl Probab 20, 487–503 (2018). https://doi.org/10.1007/s11009-017-9569-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11009-017-9569-0
Keywords
- WGCRE
- Increasing convex order
- Decreasing failure rate
- Combination mean residual waiting time
- Proportional hazard models
- Empirical WGCRE
- Risk measure