Entropy
The information entropy of the Von Mises distribution is defined as:
where is any interval of length . The logarithm of the density of the Von Mises distribution is straightforward:
The characteristic function representation for the Von Mises distribution is:
where . Substituting these expressions into the entropy integral, exchanging the order of integration and summation, and using the orthogonality of the cosines, the entropy may be written:
For, the von Mises distribution becomes the circular uniform distribution and the entropy attains its maximum value of .
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Famous quotes containing the word entropy:
“Just as the constant increase of entropy is the basic law of the universe, so it is the basic law of life to be ever more highly structured and to struggle against entropy.”
—Václav Havel (b. 1936)