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http://dx.doi.org/10.4134/CKMS.c210266

QUANTIZATION FOR A PROBABILITY DISTRIBUTION GENERATED BY AN INFINITE ITERATED FUNCTION SYSTEM  

Roychowdhury, Lakshmi (School of Mathematical and Statistical Sciences University of Texas Rio Grande Valley)
Roychowdhury, Mrinal Kanti (School of Mathematical and Statistical Sciences University of Texas Rio Grande Valley)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.3, 2022 , pp. 765-800 More about this Journal
Abstract
Quantization for probability distributions concerns the best approximation of a d-dimensional probability distribution P by a discrete probability with a given number n of supporting points. In this paper, we have considered a probability measure generated by an infinite iterated function system associated with a probability vector on ℝ. For such a probability measure P, an induction formula to determine the optimal sets of n-means and the nth quantization error for every natural number n is given. In addition, using the induction formula we give some results and observations about the optimal sets of n-means for all n ≥ 2.
Keywords
Probability measure; infinite iterated function system; optimal set; quantization error;
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