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Some results on Tsallis entropy measure and k-record values

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  • Kumar, Vikas

Abstract

Extensive or non-extensive statistical mechanics arise from the additive or non-additivity of the corresponding entropy measures. Non-additive entropy measures are important for many applications. In this article, we consider and study a non-additive Tsallis entropy for k-record statistics from some continuous probability models. Furthermore, we prove a characterization result for the Tsallis entropy of k-record values. At the end, we study Tsallis residual entropy for k-record statistics.

Suggested Citation

  • Kumar, Vikas, 2016. "Some results on Tsallis entropy measure and k-record values," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 667-673.
    • Handle: RePEc:eee:phsmap:v:462:y:2016:i:c:p:667-673
    DOI: 10.1016/j.physa.2016.05.064
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    References listed on IDEAS

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    1. Fashandi, M. & Ahmadi, Jafar, 2012. "Characterizations of symmetric distributions based on Rényi entropy," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 798-804.
    2. Kumar, Vikas, 2015. "Generalized entropy measure in record values and its applications," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 46-51.
    3. Felix Belzunce & Jorge Navarro & José M. Ruiz & Yolanda del Aguila, 2004. "Some results on residual entropy function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(2), pages 147-161, May.
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    5. Tong, S. & Bezerianos, A. & Paul, J. & Zhu, Y. & Thakor, N., 2002. "Nonextensive entropy measure of EEG following brain injury from cardiac arrest," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(3), pages 619-628.
    6. Thapliyal, Richa & Taneja, H.C. & Kumar, Vikas, 2015. "Characterization results based on non-additive entropy of order statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 297-303.
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    Cited by:

    1. Jafar Ahmadi, 2021. "Characterization of continuous symmetric distributions using information measures of records," Statistical Papers, Springer, vol. 62(6), pages 2603-2626, December.
    2. Zhang, Fode & Ng, Hon Keung Tony & Shi, Yimin, 2018. "Information geometry on the curved q-exponential family with application to survival data analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 788-802.
    3. Calì, Camilla & Longobardi, Maria & Ahmadi, Jafar, 2017. "Some properties of cumulative Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 1012-1021.
    4. Zhang, Fode & Ng, Hon Keung Tony & Shi, Yimin, 2018. "On alternative q-Weibull and q-extreme value distributions: Properties and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1171-1190.
    5. Balakrishnan, Narayanaswamy & Buono, Francesco & Longobardi, Maria, 2022. "A unified formulation of entropy and its application," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    6. Aswathy S. Krishnan & S. M. Sunoj & P. G. Sankaran, 2019. "Quantile-based reliability aspects of cumulative Tsallis entropy in past lifetime," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 17-38, January.
    7. Kumar, Vikas & Rekha,, 2018. "A quantile approach of Tsallis entropy for order statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 916-928.

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