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Poster Communications<br />
SP2<br />
Thursday, September 5th<br />
19:45<br />
Maximum Entropy distributions on the circle<br />
with given cross-moment.<br />
J. C. S. de Miranda IME/USP<br />
We determine the maximum entropy distribution on the circle, D = {(x, y) ∈ R 2 : x 2 + y 2 ≤ 1},<br />
i.e., we determine the probability density function of the bivariate random vector (X, Y ) whose<br />
image is contained in D, under the following moment and cross-moment restrictions: EX = 0,<br />
EY = 0 and EXY = m, for an arbitrary real constant m.<br />
Keywords: Maximum Entropy; Calculus of Variations; Bessel Functions<br />
100
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