All Title Author
Keywords Abstract

Generalized Entropy of Order Statistics

DOI: 10.4236/am.2012.312272, PP. 1977-1982

Keywords: Entropy, Order Statistics, Probability Integral Transformation, Residual Entropy, Generalized Information

Full-Text   Cite this paper   Add to My Lib


In this communication, we consider and study a generalized two parameters entropy of order statistics and derive bounds for it. The generalized residual entropy using order statistics has also been discussed.


[1]  B. C. Arnold, N. Balakrishnan and H. N. Nagaraja, “A First Course in Order Statistics,” John Wiley and Sons, New York, 1992.
[2]  E. H. Llyod, “Least-Squares Estimation of Location and Scale Parameters Using Order Statistics,” Biometrika, Vol. 39, No. 1-2, 1952, pp. 88-95.
[3]  E. Ataman, V. K. Aatre and K. M. Wong, “Some Statistical Properties of Median Filters,” IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. ASSP-29, No. 5, 1981, pp. 1073-1075.
[4]  K. M. Wong and S. Chen, “The Entropy of Ordered Sequences and Order Statistics,” IEEE Transactions on Information Theory, Vol. 36, No. 2, 1990, pp. 276-284. doi:10.1109/18.52473
[5]  S. Park, “The Entropy of Consecutive Order Statistics,” IEEE Transactions on Information Theory, Vol. 41, No. 6, 1995, pp. 2003-2007. doi:10.1109/18.476325
[6]  C. E. Shannon, “A Mathematical Theory of Communication,” Bell System Technical Journal, Vol. 27, 1948, pp. 379-423 and 623-656.
[7]  S. Kullback, “Information Theory and Statistics,” Wiley, New York, 1959.
[8]  N. Ebrahimi, E. S. Soofi and H. Zahedi, “Information Properties of Order Statistics and Spacings,” IEEE Transactions on Information Theory, Vol. 50, No. 1, 2004, pp. 177-183. doi:10.1109/TIT.2003.821973
[9]  N. R. Arghami and M. Abbasnejad, “Renyi Entropy Properties of Order Statistics,” Communications in Statistics, Vol. 40, No. 1, 2011, pp. 40-52. doi:10.1080/03610920903353683
[10]  A. Renyi, “On Measures of Entropy and Information,” Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Berkley, 20 June-30 July 1961, pp. 547-561.
[11]  R. S. Verma, “Generalization of Renyi’s Entropy of Order α,” Journal of Mathematical Sciences, Vol. 1, 1966, pp. 34-48.
[12]  N. Ebrahimi, “How to Measure Uncertainty in the Residual Lifetime Distributions,” Sankhya A, Vol. 58, 1996, pp. 48-57.
[13]  H. A. David and H. N. Nagaraja, “Order Statistics,” Wiley, New York, 2003. doi:10.1002/0471722162


comments powered by Disqus

Contact Us


微信:OALib Journal