Mathieu Caguiat | Searcharxiv

arXiv2024

Conditional quantization for uniform distributions on line segments and regular polygons

Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If in the quantization some of the elements in the support are preselected, then the quantization is called a conditional quantization. In this paper, we investigate the conditional quantization for the uniform distributions defined on the unit line segments and $m$-sided regular polygons, where $m\geq 3$, inscribed in a unit circle.

math.PR↗

arXiv2023

Constrained quantization for a uniform distribution

Constrained quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with a finite number of supporting points lying on a specific set. The specific set is known as the constraint of the constrained quantization. A quantization without a constraint is known as an unconstrained quantization, which traditionally in the literature is known as quantization. Constrained quantization has recently been introduced by Pandey and Roychowdhury. In this paper, for a uniform distribution with support lying on a side of an equilateral triangle, and the constraint as the union of the other two sides, we obtain the optimal sets of $n$-points and the $n$th constrained quantization errors for all positive integers $n$. We also calculate the constrained quantization dimension and the constrained quantization coefficient.

math.PR↗