On Weighted Generalized Residual Information Measure

Ashok Kumar; H C Taneja; Ashok K Chitkara; Vikas Kumar

doi:10.15415/mjis.2015.41001

Authors

Ashok Kumar Department of Mathematics, Chitkara University, Solan, India
H C Taneja Department of Applied Mathematics, D.T.U., Delhi, India
Ashok K Chitkara Department of Mathematics, Chitkara University, Solan, India
Vikas Kumar Department of Applied Sciences, UIET, M.D.U., Rohtak, India

DOI:

https://doi.org/10.15415/mjis.2015.41001

Keywords:

Shannon Entropy, Residual Entropy, Lifetime Distribution, Weighted Distribution

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.

Downloads

Download data is not yet available.

References

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.