Generalized Entropy of Order Statistics

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References

[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