Order Statistics Based Measure of Past Entropy
Abstract:
In this paper, we have proposed a measure of past entropy based on order statistics. We have studied this measure for some specific lifetime distributions. A Characterization result for the proposed measure has also been discussed and also and an upper bound for this measure has been derived.
Author(s):
DOI:
Keywords:
References:
Arghami, N.R., Abbasnejad, M. (2011). Renyi entropy properties of order statistics. Communications in Statistics, Vol. 40, 40-52. http://dx.doi.org/10.1080/03610920903353683
Arnold, B. C., Balakrishnan, N., Nagaraja, H. N., 1992. A First Course in Order Statistics. New York: John Wiley and Sons.
Baratpour, S., Ahmadi, J., Arghami, N. R., (2007). Some characterizations based on the entropy of order statistics and record values. Communications in Statistics-Theory and Methods 36: 47-57. http://dx.doi.org/10.1080/03610920600966530
Baratpour, S., Ahmadi, J., Arghami, N. R., (2008). Characterizations based on Renyi entropy of order statistics and record values. Journal of Statistical Planning and Inference, 138, 2544-2551. http://dx.doi.org/10.1016/j.jspi.2007.10.024
David, H.A., Nagaraja, H.N., (2003). Order Statistics. New York: Wiley.
Di Crescenzo, A., Lomgobardi, M. (2002). The entropy-based measure of uncertainty in past lifetime distributions. J. App. Prob.39,434-440.
Ebrahimi, N., Soofi, E.S., Zahedi, H., (2004). Information properties of order statistics and spacings. IEEE Trans. Inform. Theor vol 50, 177-183. http://dx.doi.org/10.1109/TIT.2003.821973
Ebrahimi, N., (1996). How to measure uncertainty in the residual lifetime distributions. Sankhya A 58, 48-57.
Ebrahimi, N., Kirmani, S.N.U.A., (1996). A measure of discrimination between two residual lifetime distributions and its applications. Ann. Inst. Statist. Math 48, 257-265.
Ebrahimi, N., Kirmani, S.N.U.A., (1996). Characterization of the proportional hazards model through a measure of discrimination between two residual life distributions. Biometrika 83(1), 233-235.
Kamps, U. (1998). Characterizations of distributions by recurrence relations and identities for moments of order statistics. In: N. Balakrishnan and C. R. Rao, eds. Order Statistics: Theory and Methods. Handbook of Statistics,16, 291-311. http://dx.doi.org/10.1016/S0169-7161(98)16012-1
Kullback, S. (1959). Information theory and Statistics. Wiley, New York.
Park, S. (1995). The entropy of consecutive order statistics. IEEE Trans. Inform. Theor. 41, 2003-2007. http://dx.doi.org/10.1109/18.476325
Renyi, A. (1961). On measures of entropy and information. Proc. Fourth. Berkley Symp. Math. Stat. Prob. 1960, I, University of California Press, Berkley, 547-561.
Shannon, C.E., (1948). A mathematical theory of communication. Bell syst. Tech. J. 27, 379-423 and 623-656. http://dx.doi.org/10.1002/j.1538-7305.1948.tb01338.x
Wong, K. M., Chen, S., (1990). The entropy of ordered sequences and order statistics. IEEE Trans. Inform. Theor. 36, 276-284. http://dx.doi.org/10.1109/18.52473