| Title:
|
On axiomatic characterization of entropy of type $(\alpha,\beta)$ (English) |
| Author:
|
Taneja, Inder Jeet |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
22 |
| Issue:
|
6 |
| Year:
|
1977 |
| Pages:
|
409-417 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
Entropy of type $(\alpha, \beta)$ is characterized in this paper by an axiomatic approach. It includes, in particular, a measure of type $\beta$ earlier studied by many authors. This measure has been studied also by Sharma and Taneja by generalizing a functional equation earlier considered by Chaundy and McLeod. Some properties of this measure are also studied in this paper. () |
| MSC:
|
28D20 |
| MSC:
|
94A15 |
| MSC:
|
94A17 |
| idZBL:
|
Zbl 0385.28013 |
| idMR:
|
MR0469524 |
| DOI:
|
10.21136/AM.1977.103717 |
| . |
| Date available:
|
2008-05-20T18:08:15Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103717 |
| . |
| Reference:
|
[1] T. W. Chaundy J. B. McLeod: On a functional equation.Proc. Edin. Math. Soc. Edin. Math. Notes 43 (1960), 6-7. MR 0151748 |
| Reference:
|
[2] Z. Daróczy: Generalized Information Functions.Information and Control 16 (1970), 36-51. MR 0272528, 10.1016/S0019-9958(70)80040-7 |
| Reference:
|
[3] J. Havrda F. Charvát: Quantification Method of Classification Processes. Concept of Structural a-Entropy.Kybernetika 3 (1967), 30-35. MR 0209067 |
| Reference:
|
[4] C. E. Channon: A mathematical theory of communication.B.S.T.J. 27 (1948), 379 - 423, 623-656. MR 0026286 |
| Reference:
|
[5] B. D. Sharma I. J. Taneja: Functional Measures in Information Theory.Funkcialaj Ekvacioj 17(1974), 181-191. MR 0379033 |
| Reference:
|
[6] B. D. Sharma I. J. Taneja: Entropy of type ($\alpha$, $\beta$) and other generalized measures in information theory.Metrika 22 (1975), 205-215. MR 0398670, 10.1007/BF01899728 |
| Reference:
|
[7] B. D. Sharma I. J. Taneja: Three Generalized-Additive Measures of Entropy.E. I. K. (Germany), vol. 13 (1977), 271-285. MR 0530208 |
| Reference:
|
[8] I. J. Taneja: A Joint Characterization of Shannon's Entropy and Entropy of Type $\beta$ through a Functional Equation.Journal of Mathematical Sciences (India) 10 (1975), 69-74. MR 0539497 |
| Reference:
|
[9] I. J. Taneja: On the Branching Property of Entropy.To appear in Annales Polonici Mathematici (Poland), Vol. XXXV, 1978. MR 0499877 |
| Reference:
|
[10] I. J. Taneja: A Functional Equation of Type ($\alpha$, $\beta$) in Information Theory.Communicated. |
| Reference:
|
[11] I. Vajda: Axioms for a-Entropy of a Generalized Probability Scheme.Kybernetika 2 (1968), 105-112. Zbl 0193.48201, MR 0233626 |
| . |
