A Generalization of the Havrda-Charvat and Tsallis Entropy and Its Axiomatic Characterization
In this communication, we characterize a measure of information of types α, β, and γ by taking certain axioms parallel to those considered earlier by Havrda and Charvat along with the recursive relation Hn(p1,…,pn; α, β, γ) - Hn-1(p1+p2, p3,…,pn; α, β, γ) = (A(α,γ)/(A(α,γ)-A(β,γ)))p1+p2α/γH2(p1/(p1+...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/505184 |
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| author | Satish Kumar Gurdas Ram |
| author_facet | Satish Kumar Gurdas Ram |
| author_sort | Satish Kumar |
| collection | DOAJ |
| description | In this communication, we characterize a measure of information of types α, β, and γ by taking certain axioms parallel to those considered earlier by Havrda and Charvat along with the recursive relation Hn(p1,…,pn; α, β, γ) - Hn-1(p1+p2, p3,…,pn; α, β, γ) = (A(α,γ)/(A(α,γ)-A(β,γ)))p1+p2α/γH2(p1/(p1+p2), p2/(p1+p2); α,γ) + (A(β,γ)/(A(β,γ)-A(α,γ)))(p1+p2)(β/γ)H2(p1/(p1+p2), p2/(p1+p2); γ, β), α≠γ≠β, α, β, γ>0. Some properties of this measure are also studied. This measure includes Shannon’s information measure as a special case. |
| format | Article |
| id | doaj-art-51a81adc179b4acf8c72738ce843958c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-51a81adc179b4acf8c72738ce843958c2025-02-03T01:23:19ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/505184505184A Generalization of the Havrda-Charvat and Tsallis Entropy and Its Axiomatic CharacterizationSatish Kumar0Gurdas Ram1Department of Mathematics, College of Natural Sciences, Arba Minch University, Arab Minch, EthiopiaDepartment of Applied Sciences, Maharishi Markandeshwar University, Solan, Himachal Pradesh 173229, IndiaIn this communication, we characterize a measure of information of types α, β, and γ by taking certain axioms parallel to those considered earlier by Havrda and Charvat along with the recursive relation Hn(p1,…,pn; α, β, γ) - Hn-1(p1+p2, p3,…,pn; α, β, γ) = (A(α,γ)/(A(α,γ)-A(β,γ)))p1+p2α/γH2(p1/(p1+p2), p2/(p1+p2); α,γ) + (A(β,γ)/(A(β,γ)-A(α,γ)))(p1+p2)(β/γ)H2(p1/(p1+p2), p2/(p1+p2); γ, β), α≠γ≠β, α, β, γ>0. Some properties of this measure are also studied. This measure includes Shannon’s information measure as a special case.http://dx.doi.org/10.1155/2014/505184 |
| spellingShingle | Satish Kumar Gurdas Ram A Generalization of the Havrda-Charvat and Tsallis Entropy and Its Axiomatic Characterization Abstract and Applied Analysis |
| title | A Generalization of the Havrda-Charvat and Tsallis Entropy and Its Axiomatic Characterization |
| title_full | A Generalization of the Havrda-Charvat and Tsallis Entropy and Its Axiomatic Characterization |
| title_fullStr | A Generalization of the Havrda-Charvat and Tsallis Entropy and Its Axiomatic Characterization |
| title_full_unstemmed | A Generalization of the Havrda-Charvat and Tsallis Entropy and Its Axiomatic Characterization |
| title_short | A Generalization of the Havrda-Charvat and Tsallis Entropy and Its Axiomatic Characterization |
| title_sort | generalization of the havrda charvat and tsallis entropy and its axiomatic characterization |
| url | http://dx.doi.org/10.1155/2014/505184 |
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