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Tsallis and Rényi divergences of generalized Jacobi polynomials

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  • Sfetcu, Răzvan-Cornel

Abstract

We consider some discrete probability distribution ψn(x)=(ψn,1(x),ψn,2(x),…,ψn,n(x)). We show that, under suitable conditions, the sequence of Tsallis divergence (DT(ψn(x)))n and the sequence of Rényi divergence (DR(ψn(x)))n are convergent for any x∈(−1,1).

Suggested Citation

  • Sfetcu, Răzvan-Cornel, 2016. "Tsallis and Rényi divergences of generalized Jacobi polynomials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 131-138.
    • Handle: RePEc:eee:phsmap:v:460:y:2016:i:c:p:131-138
    DOI: 10.1016/j.physa.2016.04.017
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    References listed on IDEAS

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    1. Preda, Vasile & Dedu, Silvia & Gheorghe, Carmen, 2015. "New classes of Lorenz curves by maximizing Tsallis entropy under mean and Gini equality and inequality constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 925-932.
    2. Furuichi, Shigeru & Mitroi, Flavia-Corina, 2012. "Mathematical inequalities for some divergences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 388-400.
    3. Lenzi, E.K. & Mendes, R.S. & da Silva, L.R., 2000. "Statistical mechanics based on Renyi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(3), pages 337-345.
    4. Preda, Vasile & Dedu, Silvia & Sheraz, Muhammad, 2014. "New measure selection for Hunt–Devolder semi-Markov regime switching interest rate models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 350-359.
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