Generalized Entropy of Order Statistics

ABSTRACT

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.

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.

Cite this paper

R. Thapliyal and H. Taneja, "Generalized Entropy of Order Statistics,"*Applied Mathematics*, Vol. 3 No. 12, 2012, pp. 1977-1982. doi: 10.4236/am.2012.312272.

R. Thapliyal and H. Taneja, "Generalized Entropy of Order Statistics,"

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

[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