Dynamic Cumulative Residual and Past Inaccuracy Measures

Springer Science and Business Media LLC - Tập 14 - Trang 399-412 - 2015
Vikas Kumar1, H. C. Taneja2
1Department of Applied Sciences, UIET, M. D. University, Rohtak, India
2Department of Applied Mathematics, Delhi Technological University, Delhi, India

Tóm tắt

In this paper, we have developed measures of dynamic cumulative residual and past inaccuracy. We have studied characterization results under proportional hazard model in case of dynamic cumulative residual inaccuracy and under proportional reversed hazard model in case of dynamic cumulative past inaccuracy measure. We have characterized certain specific lifetime distributions using the measures proposed. Some generalized results have also been considered.

Tài liệu tham khảo

A. Di Crescenzo, M. Longobardi, Entropy- based measure of uncertainty in past lifetime distributions, Journal of Applied Probability, 39(2002) 434–440. A. Di Crescenzo, M. Longobardi, A measure of discrimination between past lifetime distributions, Statistics and Probability Letters, 67 (2004) 173–182. A. Di Crescenzo, M. Longobardi, On cumulative entropies, Journal of Statistical Planning and Inference, 139 (12) (2009) 4072–4087. A. K. Nanda, P. Paul, Some properties of past entropy and their applications, Metrika, 64 (1) (2006) 47–61. B. Efron, Censored data and the bootstrap, Journal of the American Statistical Association, 76 (1981) 312–319. C. E. Shannon, A mathematical theory of communication, Bell System Technical Journal, (1948) 279–423 and 623–656. D. F. Kerridge, Inaccuracy and inference, Journal of Royal Statistical Society, Series B, 23 (1961) 184–194. D. R. Cox, Regression models and life tables, Journal of Royal Statistical Society, Series B, 34 (1972) 187–220. H. C. Taneja, V. Kumar, R. Srivastava, A dynamic measure of inaccuracy between two residual lifetime distributions, International Mathematical Fourm, 4(25) (2009) 1213–1220. J. Navarro, Y. D. Aguila, M. Asadi, Some new results on the cumulative residual entropy, Journal of Statistical Planning and Inference, 140(1) (2010) 310–322. M. Asadi, Y. Zohrevand, On the dynamic cumulative residual entropy, Journal of Statistical Planning and Inference, 137 (2007) 1931–1941. M. Rao, More on a new concept of entropy and information, Journal of Theoretical Probability, 18 (2005) 967–981. M. Rao, Y. Chen, B.C. Vemuri, F. Wang, Cumulative residual entropy: a new measure of information, IEEE Transactions on Information Theory, 50 (2004) 1220–1228. N. Drissi, T. Chonavel, J. M. Boucher, Generalized cumulative residual entropy for distributions with unrestricted supports, Research letters in signal processing, (2008) N. Ebrahimi, How to measure uncertainty about residual lifetime, Sankhya A, 58 (1996) 48–57. R. C. Gupta, R.D. Gupta, Proportional reversed hazards models and its applications, Journal of Statistical Planning and Inference, 137 (2007) 3525–3536. R. D. Gupta, A. K. Nanda, Some results on reversed hazard rate ordering, Communications in Statistics: Theory and Methods, 30 (2001) 2447–2457. V. Kumar, H.C. Taneja, R. Srivastava, A dynamic measure of inaccuracy between two past lifetime distributions, Metrika, 74(1) (2010) 1–10. W. J. Hall, J. A. Wellner, Mean residual life, In Statistics and Related Topics (Csrg, et al. eds), North-Holland, Amsterdam, (1981) 169–184.