×
Burbea, Jacob; Rao, C. Radhakrishna

Entropy differential metric, distance and divergence measures in probability spaces: A unified approach. (English) Zbl 0526.60015

J. Multivariate Anal. 12, 575-596 (1982).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0526.60015

Cited in 6 Reviews
Cited in 78 Documents

MSC:

60E05 Probability distributions: general theory
62H30 Classification and discrimination; cluster analysis (statistical aspects)
94A17 Measures of information, entropy
53A35 Non-Euclidean differential geometry

Keywords:

divergence measures; entropy; geodesic distance; information metric; discrimination

Citations:

Zbl 0239.60034; Zbl 0138.121; Zbl 0157.258; Zbl 0318.60013; Zbl 0479.94009; Zbl 0178.224
PDF BibTeX XML Cite
\textit{J. Burbea} and \textit{C. R. Rao}, J. Multivariate Anal. 12, 575--596 (1982; Zbl 0526.60015)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Atkinson, C; Mitchell, A.F.s, Rao’s distance measure, Sankhyā, 43, 345-365, (1981) · Zbl 0534.62012
[2] Burbea, J, The Carathéodory metric and its majorant metrics, Canad. J. math., 29, 771-780, (1977) · Zbl 0338.32015
[3] Burbea, J, A generalization of Pick’s theorem and its applications to intrinsic metrics, Ann. polon. math., 39, 49-61, (1981) · Zbl 0472.32018
[4] Burbea, J, On metrics and distortion theorems, recent developments in several complex variables, Ann. math. studies, 100, 65-92, (1981)
[5] Burbea, J; Rao, C.R, On the convexity of some divergence measures based on entropy functions, IEEE trans. information theory, IT-28, 489-495, (1982) · Zbl 0479.94009
[6] Fisher, R.A, Theory of statistical estimation, (), 700-725 · JFM 51.0385.01
[7] Havrda, M.E; Charvát, F, Quantification method of classification processes: concept of structural α-entropy, Kybernetica, 3, 30-35, (1967) · Zbl 0178.22401
[8] Kobayashi, S, ()
[9] Kullback, S; Leibler, R.A, On information and sufficiency, Ann. math. statist., 22, 79-86, (1951) · Zbl 0042.38403
[10] Matusita, K, Decision rules based on the distance, for problem of fit, two samples and estimation, Ann. math. statist., 26, 631-640, (1955) · Zbl 0065.12101
[11] Matusita, K, Decision rule based on the distance for the classification problem, Ann. inst. statist. math., 8, 67-77, (1957) · Zbl 0073.14903
[12] Pitman, E.J.G, ()
[13] Rao, C.R, Information and accuracy attainable in the estimation of statistical parameters, Bull. Calcutta math. soc., 37, 81-91, (1945) · Zbl 0063.06420
[14] Rao, C.R, On the distance between two populations, Sankhyā, 9, 246-248, (1949)
[15] Rao, C.R, Efficient estimates and optimum inference procedures in large samples (with discussion), J. roy. statist. soc. B, 24, 46-72, (1962) · Zbl 0138.13103
[16] Rao, C.R, ()
[17] Rao, C.R, Diversity and dissimilarity coefficients: a unified approach, J. theoret. pop. biology, 21, 24-43, (1982) · Zbl 0516.92021
[18] Shannon, C.E, A mathematical theory of communications, Bell system tech. J., 27, 379-423, (1948) · Zbl 1154.94303
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.