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arXiv · 1603.00731

Quantization for a probability distribution generated by an infinite iterated function system

Lakshmi Roychowdhury·Mrinal Kanti Roychowdhury
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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 $\mathbb R$. 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 $n\geq 2$.

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Lakshmi Roychowdhury, Mrinal Kanti Roychowdhury. 2016-03-02. Quantization for a probability distribution generated by an infinite iterated function system. https://arxiv.org/abs/1603.00731

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