## Abstract

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 Havrda and Charvat 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 $)$=$ (${A}_{(\mathrm{\alpha},\mathrm{\gamma})}/$(${A}_{(\mathrm{\alpha},\mathrm{\gamma})}-{A}_{(\mathrm{\beta},\mathrm{\gamma})}$))${\left({p}_{1}+{p}_{2}\right)}^{\mathrm{\alpha}/\mathrm{\gamma}}{H}_{2}({p}_{1}/({p}_{1}+{p}_{2})$, ${p}_{2}/({p}_{1}+{p}_{2})$; $\alpha $,$\gamma )+$(${A}_{(\mathrm{\beta},\mathrm{\gamma})}/{\mathrm{(A}}_{(\mathrm{\beta},\mathrm{\gamma})}-{A}_{(\mathrm{\alpha},\mathrm{\gamma})}$))${({p}_{1}+{p}_{2})}^{(\mathrm{\beta}/\mathrm{\gamma})}{H}_{2}({p}_{1}/({p}_{1}+{p}_{2})$, ${p}_{2}/({p}_{1}+{p}_{2})$; $\gamma $, $\beta $), $\alpha \ne \gamma \ne \beta $, $\alpha $, $\beta $, $\gamma >0$. Some properties of this measure are also studied. This measure includes Shannon’s information measure as a special case.

## Citation

Satish Kumar. Gurdas Ram. "A Generalization of the Havrda-Charvat and Tsallis Entropy and Its Axiomatic Characterization." Abstr. Appl. Anal. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/505184