| Title:
|
On generalized measures of relative information and inaccuracy (English) |
| Author:
|
Taneja, Inder Jeet |
| Author:
|
Gupta, H. C. |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
23 |
| Issue:
|
5 |
| Year:
|
1978 |
| Pages:
|
317-333 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
Kullback's relative information and Kerridge's inaccuracy are two information-theoretic measures associated with a pair of probability distributions of a discrete random variable. The authors study a generalized measure which in particular contains a parametric generalization of relative information and inaccuracy. Some important properties of this generalized measure along with an inversion theorem are also studied. (English) |
| Keyword:
|
generalized measures of relative information |
| Keyword:
|
inaccuracy |
| MSC:
|
94A15 |
| MSC:
|
94A17 |
| idZBL:
|
Zbl 0403.94006 |
| idMR:
|
MR0504368 |
| DOI:
|
10.21136/AM.1978.103759 |
| . |
| Date available:
|
2008-05-20T18:10:07Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103759 |
| . |
| Reference:
|
[1] Campbell L. L. (1970): Characterization of Entropy of Probability Distribution on the Real Line.- Information and Control, 21, 329-338. MR 0323447, 10.1016/S0019-9958(72)90568-2 |
| Reference:
|
[2] Gallager R. G. (1968): Information Theory and Reliable Communication.- J. Wiley and Sons, Inc., N. Y. |
| Reference:
|
[3] Hobson A. (1969): A New Theorem of Information Theory.- J. Stat. Phys., 1, 383-391. MR 0321609, 10.1007/BF01106578 |
| Reference:
|
[4] Kerridge D. F. (1961): Inaccuracy and inference.- J. Royal Stat. Soc., Ser. B 23 (1), 184 to 194. MR 0123375 |
| Reference:
|
[5] Kullback S. (1968): Information Theory and Statistics.- Dover Publi., Inc., N. Y. MR 1461541 |
| Reference:
|
[6] Rathie P. N., Pl. Kannappan (1972): A Direct-Divergence Function of Type $\beta$.- Infor- mation and Control. 22, 38 - 45. MR 0414234 |
| Reference:
|
[7] Sharma B. D., R. Autar (1973): On Characterization of a Generalized Inaccuracy Measure in Information Theory.- J. Appl. Prob. 10 464-468. MR 0389406, 10.2307/3212366 |
| Reference:
|
[8] Sharma B. D., R. Autar (1974): Relative-Information Functions and Their Type ($\alpha$, $\beta$) Generalizations.- Metrika, 21, 41 - 50. MR 0363704, 10.1007/BF01893891 |
| Reference:
|
[9] Sharma B. D., H. C. Gupta (1976): Sub-additive Measures of Relative Information and Inaccuracy.- Metrika, Vol. 23, 155-165. MR 0437211 |
| Reference:
|
[10] Sharma B. D., I. J. Taneja (1974): On Axiomatic Characterization of Information Theoretic Measures.- J. Stat. Phys., 10, 337-346. MR 0403809, 10.1007/BF01012255 |
| Reference:
|
[11] Sharma B. D., I. J. Taneja (1975): Entropy of Type ($\alpha$, $\beta$) and Other Generalized Measures in Information Theory.- Metrika, 22 (4), 205 - 215. MR 0398670, 10.1007/BF01899728 |
| Reference:
|
[12] Taneja I. J. (1974): A Joint Characterization of Directed Divergence, Inaccuracy, and Their Generalizations.- J. Statist. Phys., 11, 169-174. MR 0387861, 10.1007/BF01012518 |
| Reference:
|
[13] Taneja I. J. (1976): On Measures of Information and Inaccuracy.- J. Statist. Phys., 14, 263 - 270. MR 0403811, 10.1007/BF01023628 |
| . |
