# On one extreme value problem for entropy and error probability

On one extreme value problem for entropy and error probability The problem of determining both the maximum and minimum entropy of a random variable Y as well as the maximum absolute value of the difference between entropies of Y and another random variable X is considered under the condition that the probability distribution of X is fixed and the error probability (i.e., the probability of noncoincidence of random values of X and Y) is given. A precise expression for the minimum entropy of Y is found. Some conditions under which the entropy of Y takes its maximum value are pointed out. In other cases, some lower and upper bounds are obtained for the maximum entropy of Y as well as for the maximum absolute value of the difference between entropies of Y and X. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

# On one extreme value problem for entropy and error probability

Problems of Information Transmission, Volume 50 (3) – Oct 16, 2014
14 pages

/lp/springer_journal/on-one-extreme-value-problem-for-entropy-and-error-probability-lGMM4kb1GZ
Publisher
Springer Journals
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S003294601403016
Publisher site
See Article on Publisher Site

### Abstract

The problem of determining both the maximum and minimum entropy of a random variable Y as well as the maximum absolute value of the difference between entropies of Y and another random variable X is considered under the condition that the probability distribution of X is fixed and the error probability (i.e., the probability of noncoincidence of random values of X and Y) is given. A precise expression for the minimum entropy of Y is found. Some conditions under which the entropy of Y takes its maximum value are pointed out. In other cases, some lower and upper bounds are obtained for the maximum entropy of Y as well as for the maximum absolute value of the difference between entropies of Y and X.

### Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 16, 2014

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