Integral representations and asymptotic expansions for shannon and Renyi entropies

被引：35

作者：

Knessl, C ^{[1
]}

机构：

[1] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA

来源：

APPLIED MATHEMATICS LETTERS | 1998年 / 11卷 / 02期

关键词：

entropy; information theory; asymptotic expansions;

D O I：

10.1016/S0893-9659(98)00013-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive integral, representations for the Shannon and Renyi entropies associated with some simple probability distributions. These include the Poisson, binomial, and negative binomial distributions. Then we obtain full asymptotic expansions for the entropies.

引用

页码：69 / 74

页数：6

共 10 条

[1]

[Anonymous], 1961, P 4 BERK S MATH STAT

[2]

BLEISTEIN N, 1986, ASYMPTOTIC EXPANSION

[3] CODING FOR T-USER MULTIPLE-ACCESS CHANNELS [J].

CHANG, S ;

WELDON, EJ .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1979, 25 (06) :684-691

[4] GENERALIZED CUTOFF RATES AND RENYIS INFORMATION MEASURES [J].

CSISZAR, I .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1995, 41 (01) :26-34

[5]

Gradshteyn I.S., 1994, Tables of Integrals, Series, and Products

[6]

JACQUET P, ANAL INFORMATION THE

[7] SADDLEPOINT EXPANSIONS FOR SUMS OF MARKOV DEPENDENT-VARIABLES ON A CONTINUOUS STATE-SPACE [J].

JENSEN, JL .

PROBABILITY THEORY AND RELATED FIELDS, 1991, 89 (02) :181-199

[8]

KNESSL C, COMMUNICATION

[9] A CONVEXITY PROPERTY IN THEORY OF RANDOM-VARIABLES DEFINED ON A FINITE MARKOV-CHAIN [J].

MILLER, HD .

ANNALS OF MATHEMATICAL STATISTICS, 1961, 32 :1260-&

[10] ON FOUNDATIONS OF INFORMATION THEORY [J].

RENYI, A .

REVUE DE L INSTITUT INTERNATIONAL DE STATISTIQUE-REVIEW OF THE INTERNATIONAL STATISTICAL INSTITUTE, 1965, 33 (01) :1-+

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