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...

Full description

Saved in:
Bibliographic Details
Main Authors: Pigar Biteng, Mathieu Caguiat, Tsianna Dominguez, Mrinal Kanti Roychowdhury
Format: Article
Language:English
Published: MDPI AG 2025-03-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/13/7/1024
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849730160667918336
author Pigar Biteng
Mathieu Caguiat
Tsianna Dominguez
Mrinal Kanti Roychowdhury
author_facet Pigar Biteng
Mathieu Caguiat
Tsianna Dominguez
Mrinal Kanti Roychowdhury
author_sort Pigar Biteng
collection DOAJ
description 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 <i>m</i>-sided regular polygons, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>≥</mo><mn>3</mn></mrow></semantics></math></inline-formula>, inscribed in a unit circle.
format Article
id doaj-art-147cb433fff746c68fec8fb12f3af3b6
institution DOAJ
issn 2227-7390
language English
publishDate 2025-03-01
publisher MDPI AG
record_format Article
series Mathematics
spelling doaj-art-147cb433fff746c68fec8fb12f3af3b62025-08-20T03:08:57ZengMDPI AGMathematics2227-73902025-03-01137102410.3390/math13071024Conditional Quantization for Uniform Distributions on Line Segments and Regular PolygonsPigar Biteng0Mathieu Caguiat1Tsianna Dominguez2Mrinal Kanti Roychowdhury3School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USASchool of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USASchool of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USASchool of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USAQuantization 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 <i>m</i>-sided regular polygons, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>≥</mo><mn>3</mn></mrow></semantics></math></inline-formula>, inscribed in a unit circle.https://www.mdpi.com/2227-7390/13/7/1024probability measureconditional quantizationoptimal sets of <i>n</i>-pointsquantization dimensionquantization coefficient
spellingShingle Pigar Biteng
Mathieu Caguiat
Tsianna Dominguez
Mrinal Kanti Roychowdhury
Conditional Quantization for Uniform Distributions on Line Segments and Regular Polygons
Mathematics
probability measure
conditional quantization
optimal sets of <i>n</i>-points
quantization dimension
quantization coefficient
title Conditional Quantization for Uniform Distributions on Line Segments and Regular Polygons
title_full Conditional Quantization for Uniform Distributions on Line Segments and Regular Polygons
title_fullStr Conditional Quantization for Uniform Distributions on Line Segments and Regular Polygons
title_full_unstemmed Conditional Quantization for Uniform Distributions on Line Segments and Regular Polygons
title_short Conditional Quantization for Uniform Distributions on Line Segments and Regular Polygons
title_sort conditional quantization for uniform distributions on line segments and regular polygons
topic probability measure
conditional quantization
optimal sets of <i>n</i>-points
quantization dimension
quantization coefficient
url https://www.mdpi.com/2227-7390/13/7/1024
work_keys_str_mv AT pigarbiteng conditionalquantizationforuniformdistributionsonlinesegmentsandregularpolygons
AT mathieucaguiat conditionalquantizationforuniformdistributionsonlinesegmentsandregularpolygons
AT tsiannadominguez conditionalquantizationforuniformdistributionsonlinesegmentsandregularpolygons
AT mrinalkantiroychowdhury conditionalquantizationforuniformdistributionsonlinesegmentsandregularpolygons