Bounds on Variance for Unimodal Distributions

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We show a direct relationship between the variance and the differential entropy for subclasses of symmetric and asymmetric unimodal distributions by providing an upper bound on variance in terms of entropy power. Combining this bound with the well-known entropy power lower bound on variance, we prove that the variance of the appropriate subclasses of unimodal distributions can be bounded below and above by the scaled entropy power. As the differential entropy decreases, the variance is sandwiched between two exponentially decreasing functions in the differential entropy. This establishes that for the subclasses of unimodal distributions, the differential entropy can be used as a surrogate for concentration of the distribution.
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Issue Date
2017-11
Language
English
Article Type
Article; Proceedings Paper
Keywords

LOG-CONCAVE PROBABILITY; 20 QUESTIONS; ENTROPY

Citation

IEEE TRANSACTIONS ON INFORMATION THEORY, v.63, no.11, pp.6936 - 6949

ISSN
0018-9448
DOI
10.1109/TIT.2017.2749310
URI
http://hdl.handle.net/10203/226700
Appears in Collection
EE-Journal Papers(저널논문)
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