Maximizing the entropy of a sum of independent bounded random variables

Let X 1 ,...,X n be n independent, symmetric random variables supported on the interval [-1,1] and let S n =sigma i=1 n X i be their sum. We show that the differential entropy of S n is maximized when X 1 ,...,X n-1 are Bernoulli taking on +1 or -1 with equal probability and X n is uniformly distrib...

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Bibliographic Details
Published in:IEEE transactions on information theory 2006-05, Vol.52 (5), p.2176-2181
Main Author: Ordentlich, E.
Format: Article
Language:English
Subjects:
Applied sciences
Bounded random variables
Density measurement
differential entropy
Entropy
Exact sciences and technology
Information theory
Information, signal and communications theory
Intervals
majorization
multiple-access channel
Probability distribution
Random variables
Schur convexity
Telecommunications and information theory
Tin
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Summary:Let X 1 ,...,X n be n independent, symmetric random variables supported on the interval [-1,1] and let S n =sigma i=1 n X i be their sum. We show that the differential entropy of S n is maximized when X 1 ,...,X n-1 are Bernoulli taking on +1 or -1 with equal probability and X n is uniformly distributed
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2006.872858