Some Characterization Results Based on Dynamic Survival and Failure Entropies Abbasnejad, Maliheh;
In this paper, we develop some characterization results in terms of survival entropy of the first order statistic. In addition, we generalize the cumulative entropy recently proposed by Di Crescenzo and Logobardi (2009) to a new measure of information (called the failure entropy) and study some properties of it and its dynamic version. Furthermore, power distribution is characterized based on dynamic failure entropy.
First order statistic;power distribution;mean past life function;reversed Hazard function;
Some Results on Dynamic Generalized Survival Entropy, Communications in Statistics - Theory and Methods, 2015, 44, 8, 1653
Bivariate Extension of (Dynamic) Cumulative Past Entropy, Communications in Statistics - Theory and Methods, 2016, 0
Weighted Entropies and Their Estimations, Communications in Statistics - Simulation and Computation, 2016, 0
On generalized dynamic survival and failure entropies of order , Statistics & Probability Letters, 2015, 96, 123
Abbasnejad, M., Arghami, N. R., Morgenthaler, S. and Mohtashami Borzadaran, G. R. (2010). On the dynamic survival entropy, Statistics and Probability Letters, 80, 1962-1971.
Abraham, B. and Sankaran, P. G. (2005). Penyi's entropy for residual lifetime distribution, Statistical Paper, 46, 17-30.
Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1992). A First Course in Order Statistics, John Wiley & Sons, New York.
Asadi, M., Ebrahimi, N. and Soofi, E. S. (2005). Dynamic generalized information measures, Statistics and Probability Letters, 71, 85-98.
Asadi, M. and Zohrevand, Y. (2007). On the dynamic cumulative residual entropy, Journal of Statistical Planning and Inference, 137, 1931-1941.
Baratpour, S. (2010). Characterization based on cumulative residual entropy of first order ststistics, Communications in Statistics: Theory and Methods, 39, 3645-3651.
Baratpour, S., Ahmadi, J. and Arghami, N. R. (2008). Some characterization based on Renyi entropy of order statistics and record values, Journal of Statistical Planning and Inference, 138, 2544-2551.
David, H. A. and Nagaraja, H. N. (2003). Order Statistics, John Wiley & Sons, New York.
Di Crescenzo, A. and Longobardi, M. (2002). Entropy-based measure of uncertainty in past lifetime distributions, Journal of Applied Probability, 39, 434-440.
Di Crescenzo, A. and Longobardi, M. (2004). A measure of discrimination between past lifetime distributions, Statistics and Probability Letters, 67, 173-182.
Di Crescenzo, A. and Longobardi, M. (2009). On cumulative entropies, Journal of Statistical Planning and Inference, 139, 4072-4087.
Ebrahimi, N. (1996). How to measure uncertainty in the residual lifetime distributions, Sankhya, 58, 48-57.
Gertsbakh, I. and Kagan, A. (1999). Characterization of the Weibull distribution by properties of the Fisher information under type I censoring, Statistics and Probability Letters, 42, 99-105.
Kamps, U. (1998). Characterizations of distributions by recurrence relations and identities for moments of order statistics, In Order Statistics: Theory and Methods. Handbook of Statistics, Balakrishnan, N., Rao, C. R., Eds. 16, Amesterdam: Elsevier, 291-311.
Nanda, A. K. and Paul, P. (2006). Some properties of past entropy and their applications, Metrika, 64, 47-61.
Nanda, A. K., Singh, H., Misra, N. and Paul, P. (2003). Reliability properties of reversed residual lifetime, Communications in Statistics: Theory and Methods, 32, 2031-2042.
Rao, M. (2005). More on a new concept of netropy and information, Journal of Theoretical Probability, 18, 967-981.
Rao, M., Chen, Y., Vemuri, B.C. and Wang, F. (2004). Cumulative residual entropy: A new measure of information, IEEE Transactions on Information Theoty, 50, 1220-1228.
Renyi, A. (1961). On measures of entropy and information, In Proceeding of the Fourth Berkeley Symposium, I, UC Press, Berkeley, 547-561.
Shannon, C. E. (1948). A mathematical theory of communication, Bell System Technology, 27, 379-423.
Wang, F. and Vemuri, B. C. (2007). Non-rigid multi-model image registration using cross-cumulative residual entropy, International Journal of Computer Vision, 74, 201-215.
Zheng, G. (2001). A characterization of the factorization of hazard function by the Fisher information under type II censoring with application to the Weibull family, Statistics and Probability Letters, 52, 249-253.
Zografos, K. and Nadarajah, S. (2005). Survival exponential entropies, IEEE Transactions on Information Theory, 51, 1239-1246.