Mutual Dependence of Random Variables and Maximum Discretized Entropy
Bertoluzza, Carlo ; Forte, Bruno
Ann. Probab., Tome 13 (1985) no. 4, p. 630-637 / Harvested from Project Euclid
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In connection with a random vector $(X, Y)$ in the unit square $Q$ and a couple $(m, n)$ of positive integers, we consider all discretizations of the continuous probability distribution of $(X, Y)$ that are obtained by an $m \times n$ cartesian decomposition of $Q$. We prove that $Y$ is a (continuous and invertible) function of $X$ if and only if for each $m, n$ the maximum entropy of the finite distributions equals $\log(m + n - 1)$
Publié le : 1985-05-14
Classification:  62-07,  Entropy,  discretization,  mutual dependence,  60E99,  62B10 
@article{1176993016,
     author = {Bertoluzza, Carlo and Forte, Bruno},
     title = {Mutual Dependence of Random Variables and Maximum Discretized Entropy},
     journal = {Ann. Probab.},
     volume = {13},
     number = {4},
     year = {1985},
     pages = { 630-637},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993016}
}

Bertoluzza, Carlo; Forte, Bruno. Mutual Dependence of Random Variables and Maximum Discretized Entropy. Ann. Probab., Tome 13 (1985) no. 4, pp.  630-637. http://gdmltest.u-ga.fr/item/1176993016/