Some Results on Quantile-based Dynamic Survival and Failure Tsallis Entropy
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Abstract
Non-additive entropy measures are important for many applications. In this paper, we introduce a quantile-based non-additive entropy measure, based on Tsallis entropy and study their properties. Some relationships of this measure with well-known reliability mea- sures and ageing classes are studied and some characterization results are presented. Also the concept of quantile-based shift independent entropy measures has been introduced and studied various properties.
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References
M. Abbasnejad, N. R. Arghami, S. Morgenthaler and G. R. Mohtashami Borzadaran, On the dynamic survival entropy, Statistics and Probability Letters, 80(2010), 1962-1971.
M. Asadi, N. Ebrahimi and E. S. Soofi, Dynamic generalized information measures, Statistics and Probability Letters, 71 (2005), 85-98.
M. Asadi and Y. Zohrevand, On the dynamic cumulative residual entropy, Journal of Sta- tistical Planning and Inference, 137(6), (2007), 1931-1941.
M. Belis and S. Guiasu, A qualitative measure of information in cybernatic systems, IEEE Transactions on Information Theory, 4 (1968), 593-594.
S. Das, On weighted generalized entropy, Communications in Statistics-Theory and Meth- ods, 46(12)(2017), 5707-5727.
A. Di Crescenzo, M. Longobardi, On weighted residual and past entropies, Scientiae Math- ematicae Japonicae, 64 (2006), 255-266.
A. Di Crescenzo, M. Longobardi, On cumulative entropies, Journal of Statistical Planning and Inference, 139(12)(2009), 4072-4087.
N. Ebrahimi, How to measure uncertainty in the residual lifetime distribution, Sankhyã Ser. A, 58 (1996), 48-56.
W. Gilchrist, Statistical modelling with quantile functions, Chapman and Hall, CRC, Boca Raton, FL, 2000.
V. H. Hamity and D. E. Barraco, Generalized nonextensive thermodynamics applied to the cosmical background radiation in Robertson-Walker universe, Physical Review Letter, 76 (1996), 4664-4666.
R. K. S. Hankin and A. Lee, A new family of nonnegative distributions, Australian and New Zealand Journal of Statistics, 48(2006) 67-78.
J. Havrda and F. Charvat, Quantification method of classification process: concept of structural α-entropy, Kybernetika, 3 (1967), 30-35.
S. Kayal and R. Moharana, On weighted cumulative residual entropy, Journal of Statistics and Management Systems, 20 (2017), 153-173.
S. Kayal and M. R. Tripathy, A quantile-based Tsallis-α divergence, Physica A: Statistical Mechanics and its Applications, 492 (2018), 496-505.
A. H. Khammar and S. M. A. Jahanshahi, On weighted cumulative residual Tsallis entropy and its dynamic version, Physica -A Statistical Mechanics and its Applications, 491 (2018), 678-692.
A. S. Krishanan, S. M. Sunoj and P. G. Sankaran, Quantile-based reliability aspects of cumulative Tsallis entropy in past lifetime, Metrika, 82(1) (2018), 17-38.
V. Kumar,Tsallis entropy measure and k-record values, Physica-A Statistical Mechanics and its Applications, 462(2016), 667-673.
V. Kumar and Rekha, Quantile approach of dynamic generalized entropy (divergence) measure, Statistica, 78(2)(2018), 105-126.
V. Kumar and H. C. Taneja, On length biased dynamic measure of past inaccuracy, Metrika, 75 (1) (2012), 73-84.
V. Kumar and H. C. Taneja, A generalized entropy-based residual lifetime distributions, International Journal of Biomathematics, 4(2) (2011), 171-184.
M. Mirali, S. Baratpour and V. Fakoor, On weighted cumulative residual entropy, Communications in Statistics-Theory and Methods, 46(6) (2017), 2857-2869.
F. Misagh, Y. Panahi, G.H. Yari and R. Shahi, Weighted cumulative entropy and its estima- tion. In: 2011 IEEE International Conference on Quality and Reliability (ICQR), (2011), doi:10.1109/ICQR.2011.6031765
N. U. Nair, P. G. Sankaran and N. Balakrishnan, Quantile-based reliability analysis, New York: Springer, 2013.
N. U. Nair and P. G. Sankaran, Quantile-based reliability analysis, Communications in Statistics Theory and Methods, 38(2) (2009), 222-232.
A. K. Nanda and P. Paul, Some results on generalized residual entropy, Information Sciences, 176(1) (2006), 27-47.
A. K. Nanda, P. G. Sankaran and S.M. Sunoj, Residual Renyi entropy : a quantile qpproach, Statistics and Probability Letters, 85 (2014), 114-121.
G. Rajesh and S.M. Sunoj, Some properties of cumulative Tsallis entropy of order α, Statistical papers, (2016), 1-11.
M. Rao, Y. Chen, B. C. Vemuri and F. Wang, Cumulative residual entropy : a new measure of information, IEEE Transactions on Information Theory, 50(6) (2004), 1220-1228.
M. Rao, More on a new concept of entropy and information, Journal of Theoretical Probability, 18 (2005), 967-981.
S. Tong, A. Bezerianos, J. Paul, Y. Zhu and N. Thakor, Nonextensive entropy measure of EEG following brain injury from cardiac arrest, Physica A: Statistical Mechanics and its Ap- plications, 305(3-4) (2002), 619-628.
C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, Journal Statistical Physics, 52(1-2) (1988), 479-487.
P. G. Sankaran and S.M. Sunoj, Quantile-based cumulative entropies, Communications in Statistics Theory and Methods, 46(2) (2017), 805-814.
M. M. Sati and N. Gupta, Some characterization results on dynamic cumulative residual Tsallis entropy, Journal of probability and statistics, (2015), Article ID 694203, 8 Pages, http://dx.doi.org/10.1155/2015/694203.
C. E. Shannon, A mathematical theory of communication, Bell System Technical Journal, 27 (1948), 379-423.
S. M. Sunoj and P. G. Sankaran, Quantile-based entropy function, Statistics and Probability Letters, 82 (2012), 1049-1053.
S. M. Sunoj, A. S. Krishnan and P. G. Sankaran, A quantile-based study of cumulative residual Tsallis entropy measures, Physica A: Statistical Mechanics and its Applications, 494 (2017), 410-421.
S. M. Sunoj, P. G. Sankaran and A. K. Nanda, Quantile-based entropy function in past life- time, Statistics and Probability Letters, 83(1) (2013), 366-372.
F. Wang and B. C. Vemuri, Non-Rigid multimodal image registration using cross-cumulative residual entropy, International Journal of Computer Vision, 74(2) (2007), 201-215.
M. Yu, C. Zhanfang, and Z. Hongbiao, Research of automatic medical image segmenta- tion algorithm based on Tsallis entropy and improved PCNN., IEEE proceedings on ICMA, (2009), 1004-1008.