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.
Roychowdhury, Lakshmi, and Mrinal Kanti Roychowdhury. “QUANTIZATION FOR A PROBABILITY DISTRIBUTION GENERATED BY AN INFINITE ITERATED FUNCTION SYSTEM.” Communications of the Korean Mathematical Society, vol. 37, no. 3, 대한수학회, July 2022, pp. 765–800, doi:10.4134/CKMS.C210266.
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Communications of the Korean Mathematical Society