Commun. Korean Math. Soc. 2022; 37(3): 765-800
Online first article May 24, 2022 Printed July 31, 2022
https://doi.org/10.4134/CKMS.c210266
Copyright © The Korean Mathematical Society.
Lakshmi Roychowdhury, Mrinal Kanti Roychowdhury
University of Texas Rio Grande Valley; University of Texas Rio Grande Valley
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 $mathbb R$. For such a probability measure $P$, an induction formula to determine the optimal sets of $n$-means and the $n$th 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 $ngeq 2$.
Keywords: Probability measure, infinite iterated function system, optimal set, quantization error
MSC numbers: Primary 60Exx, 28A80, 94A34
Supported by: The research of the second author was supported by U.S. National Security Agency (NSA) Grant H98230-14-1-0320.
2023; 38(2): 431-450
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