Constrained quantization for a uniform distribution
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909381187076096 |
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| author | Biteng, Pigar Caguiat, Mathieu Deb, Dipok Roychowdhury, Mrinal Kanti Villanueva, Beatriz Vela |
| author_facet | Biteng, Pigar Caguiat, Mathieu Deb, Dipok Roychowdhury, Mrinal Kanti Villanueva, Beatriz Vela |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16615 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Constrained quantization for a uniform distribution Biteng, Pigar Caguiat, Mathieu Deb, Dipok Roychowdhury, Mrinal Kanti Villanueva, Beatriz Vela Probability 60Exx, 94A34 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. |
| title | Constrained quantization for a uniform distribution |
| topic | Probability 60Exx, 94A34 |
| url | https://arxiv.org/abs/2312.16615 |