Title:
|
Generalized Jensen difference based on entropy functions (English) |
Author:
|
Sahoo, Prasanna K. |
Author:
|
Wong, A. K. C. |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 |
Volume:
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24 |
Issue:
|
4 |
Year:
|
1988 |
Pages:
|
241-250 |
. |
Category:
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math |
. |
MSC:
|
62B10 |
MSC:
|
68T10 |
MSC:
|
94A17 |
idZBL:
|
Zbl 0667.62003 |
idMR:
|
MR961558 |
. |
Date available:
|
2009-09-24T18:06:43Z |
Last updated:
|
2012-06-05 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/124415 |
. |
Reference:
|
[1] S. Arimoto: Information theoretic considerations of estimations problems.Inform. and Control 19 (1971), 181-194. MR 0309224 |
Reference:
|
[2] M. Behara, J. S. Chawla: Generalized $\gamma$-entropy.Entropy and ergodic theory, pp. 15-38. Selecta Statistica Canadiana, Vol. 2, Univ. Press Canada, Toronto, Ontario 1975. Zbl 0358.94028, MR 0389399 |
Reference:
|
[3] M. Ben-Bassat: $f$-Entropies, probability of error, and feature selection.Inform. and Control 39 (1978), 227-242. Zbl 0394.94011, MR 0523439 |
Reference:
|
[4] J. Burbea, C. R. Rao: On the convexity of some divergence measures based on entropy functions.IEEE Trans. Inform. Theory IT-28 (1982), 489-495. Zbl 0479.94009, MR 0672884 |
Reference:
|
[5] J. Burbea, C. R. Rao: On the convexity of higher order Jensen differences based on entropy functions.IEEE Trans. Inform. Theory IT-28 (1982), 961-963. Zbl 0497.94002, MR 0687297 |
Reference:
|
[6] R. Chakraborty: A note on Nei's measure of gene diversity in a substructured population.Humangenetik 21 (1974), 85-88. |
Reference:
|
[7] Z. Daróczy: Generalized information functions.Inform. and Control 16 (1970), 36-51. MR 0272528 |
Reference:
|
[8] A. El-Sayed: A generalized entropy form of the Fano inequality.Utilitas Math. 12 (1977), 289-298. Zbl 0386.94005, MR 0479673 |
Reference:
|
[9] R. G. Gallager: Information Theory and Reliable Communication.Wiley, New York 1968. Zbl 0198.52201 |
Reference:
|
[10] J. Havrda, F. Charvát: Quantification method of classification process, concept of structural $\alpha$-entropy.Kybernetika 3 (1967), 30-35. MR 0209067 |
Reference:
|
[11] N. Jardine, R. Sibson: Mathematical Taxonomy.Wiley, New York 1971. Zbl 0322.62065, MR 0441395 |
Reference:
|
[12] L. Kanal: Patterns in pattern recognition: 1968--1974.IEEE Trans. Inform. Theory IT-20 (1974), 697-722. Zbl 0286.68055, MR 0356609 |
Reference:
|
[13] R. C. Lewotin: The apportionment of human diversity.Evolutionary Biology 6 (1972), 381-398. |
Reference:
|
[14] T. K. Nayak: On diversity measures based on entropy functions.Comm. Statist. A 14 (1985), 203-215. Zbl 0561.62004, MR 0788794 |
Reference:
|
[15] T. K. Nayak: Sampling distributions in analysis of diversity.Sankhya Ser. B 48 (1986), 1-9. Zbl 0656.62024, MR 0887681 |
Reference:
|
[16] M. Nei: Analysis of gene diversity in subdivided populations.Proc. Nat. Acad. Sci. 70 (1973), 3321-3323. Zbl 0272.92013 |
Reference:
|
[17] C. R. Rao: Diversity and dissimilarity coefficients: A unified approach.J. Theor. Pop. Biol. 27 (1982), 24-43. Zbl 0516.92021, MR 0662520 |
Reference:
|
[18] C. R. Rao: Convexity properties of entropy function and analysis of diversity.In: Inequalities in Statistics and Probability (Y. L. Tong, ed.). IMS Lecture Notes, 1984, Vol. 5, pp. 68-77. MR 0789236 |
Reference:
|
[19] A. Rényi: On measures of entropy and information.In: Proc. Fourth Berkeley Symp. 1960, Vol. 1, Univ. of California Press, Berkeley--Los Angeles 1961, pp. 547-561. MR 0132570 |
Reference:
|
[20] P. K. Sahoo: On the monotonicity of generalized gamma entropy.Submitted to Bull. Inst. Math. Acad. Sinica (1985). |
Reference:
|
[21] P. K. Sahoo: On a generalization of Shannon's random cipher result.Kybernetika 22 (1986), 385-392. Zbl 0618.94007, MR 0871601 |
Reference:
|
[22] C. E. Shannon: Mathematical theory of communication.Bell Systems Tech. J. 27 (1948), 379-423. Zbl 1154.94303, MR 0026286 |
Reference:
|
[23] R. Sibson: Information radius.Z. Wahrsch. Verw. Gebiete 14 (1969), 149-160. Zbl 0186.53301, MR 0258198 |
Reference:
|
[24] I. Vajda: Bounds of the minimal error probability on checking a finite or countable number of hypotheses.Problems Inform. Transmissions 4 (1968), 6-14. MR 0267685 |
Reference:
|
[25] A. K. C. Wong, M. L. You: Distance and entropy measure of random graph with application to structural pattern recognition.IEEE Trans. Pattern Anal. Mach. Intell. PAMI-7 (1985), 599-609. |
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