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...
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MDPI AG
2025-03-01
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| 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. |
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| language | English |
| publishDate | 2025-03-01 |
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| 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 |
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