A generalization of the Havrda-Charvat and Tsallis entropy and its axiomatic characterization. (English) Zbl 1472.94038

Kumar, Satish; Ram, Gurdas

Abstr. Appl. Anal. 2014, Article ID 505184, 8 p. (2014).

Summary: In this communication, we characterize a measure of information of types \(\alpha, \beta\), and \(\gamma\) by taking certain axioms parallel to those considered earlier by J. Havrda and F. Charvát [Kybernetika 3, 30–35 (1967; Zbl 0178.22401)] along with the recursive relation \(H_n(p_1,\dots,p_n;\alpha,\beta,\gamma)-H_{n-1}(p_1+p_2,p_3,\dots,p_n; \alpha,\beta,\gamma)=(A_{(\alpha,\gamma)}/(A_{(\alpha,\gamma)}-A_{(\beta,\gamma)}))(p_1+p_2)^{\alpha/\gamma}H_2(p_1/(p_1+p_2), p_2/(p_1+p_2);\alpha,\gamma)+(A_{(\beta,\gamma)}/(A_{(\beta,\gamma)}-A_{(\alpha,\gamma)}))(p_1+p_2)^{(\beta/\gamma)}H_2(p_1/(p_1+p_2)\), \(p_2/(p_1+p_2);\gamma,\beta)\), \(\alpha\neq\gamma\neq\beta\), \(\alpha,\beta,\gamma>0\). Some properties of this measure are also studied. This measure includes Shannon’s information measure as a special case.

MSC:

94A17	Measures of information, entropy
94A20	Sampling theory in information and communication theory

Keywords:

measure of information of types; Shannon’s information measure

Citations:

Zbl 0178.22401

References:

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