Bounds on variance for symmetric unimodal distributions

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We show a direct relationship between the variance and the differential entropy for the general class of symmetric 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 for the general class of symmetric unimodal distributions the variance can be bounded below and above by the scaled entropy power. As differential entropy decreases, the variance is sandwiched between two exponentially decreasing functions in the differential entropy. This establishes that for the general class of symmetric unimodal distributions, the differential entropy can be used as a surrogate for concentration of the distribution.
Publisher
Institute of Electrical and Electronics Engineers Inc.
Issue Date
2015-10-01
Language
English
Citation

53rd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2015, pp.1235 - 1240

DOI
10.1109/ALLERTON.2015.7447149
URI
http://hdl.handle.net/10203/225740
Appears in Collection
EE-Conference Papers(학술회의논문)
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