Conditional Optimal Sets and the Quantization Coefficients for Some Uniform Distributions
Bucklew and Wise (1982) showed that the quantization dimension of an absolutely continuous probability measure on a given Euclidean space is constant and equals the Euclidean dimension of the space, and the quantization coefficient exists as a finite positive number. By giving different examples, in...
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2025-07-01
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| author | Evans Nyanney Megha Pandey Mrinal Kanti Roychowdhury |
| author_facet | Evans Nyanney Megha Pandey Mrinal Kanti Roychowdhury |
| author_sort | Evans Nyanney |
| collection | DOAJ |
| description | Bucklew and Wise (1982) showed that the quantization dimension of an absolutely continuous probability measure on a given Euclidean space is constant and equals the Euclidean dimension of the space, and the quantization coefficient exists as a finite positive number. By giving different examples, in this paper, we have shown that the quantization coefficients for absolutely continuous probability measures defined on the same Euclidean space can be different. We have taken uniform distribution as a prototype of an absolutely continuous probability measure. In addition, we have also calculated the conditional optimal sets of <i>n</i>-points and the <i>n</i>th conditional quantization errors for the uniform distributions in constrained and unconstrained scenarios. |
| format | Article |
| id | doaj-art-b6cdfc6d0ff941c6b6d0966b205af3b5 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-b6cdfc6d0ff941c6b6d0966b205af3b52025-08-20T04:00:55ZengMDPI AGMathematics2227-73902025-07-011315235010.3390/math13152350Conditional Optimal Sets and the Quantization Coefficients for Some Uniform DistributionsEvans Nyanney0Megha Pandey1Mrinal Kanti Roychowdhury2School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USASchool of Mathematics, Northwest University, Xi’an 710069, ChinaSchool of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX 78539-2999, USABucklew and Wise (1982) showed that the quantization dimension of an absolutely continuous probability measure on a given Euclidean space is constant and equals the Euclidean dimension of the space, and the quantization coefficient exists as a finite positive number. By giving different examples, in this paper, we have shown that the quantization coefficients for absolutely continuous probability measures defined on the same Euclidean space can be different. We have taken uniform distribution as a prototype of an absolutely continuous probability measure. In addition, we have also calculated the conditional optimal sets of <i>n</i>-points and the <i>n</i>th conditional quantization errors for the uniform distributions in constrained and unconstrained scenarios.https://www.mdpi.com/2227-7390/13/15/2350probability measureconditional quantizationoptimal sets of <i>n</i>-pointsquantization coefficient |
| spellingShingle | Evans Nyanney Megha Pandey Mrinal Kanti Roychowdhury Conditional Optimal Sets and the Quantization Coefficients for Some Uniform Distributions Mathematics probability measure conditional quantization optimal sets of <i>n</i>-points quantization coefficient |
| title | Conditional Optimal Sets and the Quantization Coefficients for Some Uniform Distributions |
| title_full | Conditional Optimal Sets and the Quantization Coefficients for Some Uniform Distributions |
| title_fullStr | Conditional Optimal Sets and the Quantization Coefficients for Some Uniform Distributions |
| title_full_unstemmed | Conditional Optimal Sets and the Quantization Coefficients for Some Uniform Distributions |
| title_short | Conditional Optimal Sets and the Quantization Coefficients for Some Uniform Distributions |
| title_sort | conditional optimal sets and the quantization coefficients for some uniform distributions |
| topic | probability measure conditional quantization optimal sets of <i>n</i>-points quantization coefficient |
| url | https://www.mdpi.com/2227-7390/13/15/2350 |
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