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Quantization For Infinite Affine Transformations, Dogan Comez, Mrinal Kanti Roychowdhury
Quantization For Infinite Affine Transformations, Dogan Comez, Mrinal Kanti Roychowdhury
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite set. In this article, we consider a probability distribution generated by an infinite system of affine transformations {S-ij} on R-2 with associated probabilities {p(ij)} such that p(ij) > 0 for all i, j is an element of N and Sigma(infinity)(i,j=1) p(ij) = 1. For such a probability measure P, the optimal sets of n-means and the nth quantization error are calculated for every natural number n. It is shown that the distribution of such a probability measure is the …