On Weighted Generalized Residual Information Measure
Abstract:
In this paper, we have proposed the concept of weighted generalized residual entropy of order α and type β, and have shown that the proposed measure characterizes the distribution function uniquely.
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Baig, M. A. K. and Dar, J. G. (2008), Generalized Residual Entropy Function and Its Applications, European Journal of Pure and Applied Mathematics, vol. 1, no. 4, pp. 30-40.
Belis, M. and Guiasu, S. (1968), A Quantitative-qualitative Measure of Information in Cybernetic Systems, IEEE Transactions on Information Theory vol. 14, issue 4, pp. 593-594. http://dx.doi.org/10.1109/TIT.1968.1054185
Crescenzo, A. D. and Longobardi, M. (2006), On Weighted Residual and Past Entropies, Scientiae Mathematicae Japonicae 64, no. 2, pp. 255-266.
Das, S. (2014), On Weighted Generalized Entropy, Communications in Statistics-Theory and Methods (Accepted).
E Ebrahimi, N. (1996), How to Measure Uncertainty in The Residual Life Time Distribution, Sankhyã: The Indian Journal of Statistics, vol. 58, Series A, Pt. 1, pp. 48-56.
Fisher, R. A. (1934), The Effects of Methods of Ascertainment upon The Estimation of Frequencies, The Annals of Eugenics 6, 13-25. http://dx.doi.org/10.1111/j.1469-1809.1934.tb02105.x
Ghitany, M. E. and Al-Mutairi, D. K. (2008), Size-based Poisson-Lindley Distribution and its Application, METRON-International Journal of Statistics, vol. LXVI, n. 3, pp. 299-311.
Guiasu, S. (1986), Grouping Data by Using The Weighted Entropy, Journal of Statistical Planning and Inference, 15, pp. 63-69. http://dx.doi.org/10.1016/0378-3758(86)90085-6
H Havrda, J. and Charvat, F. (1967), Quantification Method of Classification Process: Concept of Structural α-entropy, Kybernetika, vol.3, pp. 30-35.
K Kareema, A. K. and Ahmad, F. H. (2013), Double Weighted Distribution and Double Weighted Exponential Distribution, Mathematical Theory and Modeling, vol. 3, no. 5, pp 124-134.
K Khinchin, A. J. (1957), Mathematical Foundation of Information Theory, Dover, New York.
K Kumar, V., et al. (2010), Length Biased Weighted Residual Inaccuracy Measure, METRON-International Journal of Statistics, vol. LXVIII, no. 2, pp. 153-160. http://dx.doi.org/ 10.1007/BF03263532
Nanda, A. K. and Paul, P. (2006), Some Results on Generalized Residual Entropy, Information Sciences, 176, pp. 27-47. http://dx.doi.org/10.1016/j.ins.2004.10.008
Oluyede, B. O. and Terbeche, M. (2007), On Energy and Expected Uncertainty Measures in Weighted Distributions International Mathematical Forum, 2, no. 20, 947-956
Psarrakos, G. and Navarro, J. (2013), Generalized Cumulative Residual Entropy and Record Values, Metrika vol. 76, pp. 623-640. http://dx.doi.org/10.1007/s00184-012-0408-6
R Rao, C. R. (1965), On Discrete Distributions Arising out of Methods of Ascertainment, Sankhy: The Indian Journal of Statistics, Series A (1961-2002), vol. 27, no. 2/4, pp. 311-324.
R Renyi, A. (1961), On Measure of Entropy and Information, Proceedings of the 4th Berkeley symposium on mathematical statistical and probability, vol.1, pp.547-561.
Shannon, C. E. (1948), A Mathematical Theory of Communication, Bell System Technical Journal, vol. 27, pp. 379-423, 623-656.
Sunoj, S. M. and Linu, M. N. (2012), Dynamic Cumulative Residual Renyi’s Entropy, Statistics: A Journal of Theoretical and Applied Statistics, 46:1, 41-56. http://dx.doi.org/10.1080/ 02331888.2010.494730
Taneja, H. C., et al. (2009), A Dynamic Measure of Inaccuracy between Two Residual Lifetime Distributions, International Mathematical Forum, 4, 2009, no. 25, pp. 1213-1220.
Verma, R. S. (1966), Generalizations of Renyi’s Entropy of order α, Journal of Mathematical Sciences, vol.1, pp.34-48.
