Optimal quantizers for a nonuniform distribution on a Sierpinski carpet

Mrinal Kanti Roychowdhury

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arXiv · 1605.02281

Optimal quantizers for a nonuniform distribution on a Sierpinski carpet

Mrinal Kanti Roychowdhury

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Abstract

The purpose of quantization for a probability distribution is to estimate the probability by a discrete probability with finite support. In this paper, a nonuniform probability measure $P$ on $\mathbb R^2$ which has support the Sierpi\'nski carpet generated by a set of four contractive similarity mappings with equal similarity ratios has been considered. For this probability measure, the optimal sets of $n$-means and the $n$th quantization errors are investigated for all $n\geq 2$.

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Mrinal Kanti Roychowdhury. 2016-05-08. Optimal quantizers for a nonuniform distribution on a Sierpinski carpet. https://arxiv.org/abs/1605.02281

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