Order Statistics Based Measure of Past Entropy

Richa Thapliyal and H.C.Taneja


Order Statistics, Past entropy, Reversed hazard rate, Survival function.


In this paper we have proposed a measure of past entropy based on order statistics. We have studied this measure for some specific life- time distributions. A Characterization result for the proposed measure has also been discussed and also and an upper bound for this measure has been derived

URL http://dspace.chitkara.edu.in/jspui/bitstream/1/110/1/12013_MJIS_Richa.pdf
DOI 10.15415/mjis.2013.12013
  • Arghami, N.R.,Abbasnejad,M.(2011).Renyi entropy properties of order statistics. Communications in Statistics, V ol. 40, 40-52.
  • 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 entropy of order statistics and record values. Communications in Statistics -Theory and Methods 36: 47-57.
  • Baratpour, S., Ahmadi, J., Arghami, N. R., (2008). Characterizations based on Renyien tropy of order statistics and record values. Journal of Statistical Planning and Inference, 138, 2544-2551.
  • David, H.A., Nagaraja, H.N., (2003). Order Statistics. New York : Wiley.
  • Di Crescenzo, A., Lomgobardi, M. (2002). 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. In form. Theor vol 50, 177-183.
  • 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). A characterization of the propotional 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.
  • 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.
  • 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.
  • Wong, K. M., Chen, S., (1990). The entropy of ordered sequences and order statistics. IEEE Trans. Inform. Theor. 36, 276-284