Conditional Quantization for Uniform Distributions on Line Segments and Regular Polygons

Pigar Biteng, Mathieu Caguiat, Tsianna Dominguez and Mrinal Kanti Roychowdhury ()
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Pigar Biteng: School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USA
Mathieu Caguiat: School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USA
Tsianna Dominguez: School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USA
Mrinal Kanti Roychowdhury: School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USA

Mathematics, 2025, vol. 13, issue 7, 1-17

Abstract: 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 ≥ 3 , inscribed in a unit circle.

Keywords: probability measure; conditional quantization; optimal sets of n -points; quantization dimension; quantization coefficient (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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