Optimal quantization for a probability measure on a nonuniform stretched Sierpiński triangle
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2016
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| _version_ | 1866918035331219456 |
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| author | Pandey, Megha Roychowdhury, Mrinal Kanti |
| author_facet | Pandey, Megha Roychowdhury, Mrinal Kanti |
| contents | 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. In this paper, we have considered a Borel probability measure $P$ on $\mathbb R^2$, which has support a nonuniform stretched Sierpiński triangle generated by a set of three contractive similarity mappings on $\mathbb R^2$. For this probability measure, we investigate the optimal sets of $n$-means and the $n$th quantization errors for all positive integers $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1606_00963 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Optimal quantization for a probability measure on a nonuniform stretched Sierpiński triangle Pandey, Megha Roychowdhury, Mrinal Kanti Information Theory 60Exx, 28A80, 94A34 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. In this paper, we have considered a Borel probability measure $P$ on $\mathbb R^2$, which has support a nonuniform stretched Sierpiński triangle generated by a set of three contractive similarity mappings on $\mathbb R^2$. For this probability measure, we investigate the optimal sets of $n$-means and the $n$th quantization errors for all positive integers $n$. |
| title | Optimal quantization for a probability measure on a nonuniform stretched Sierpiński triangle |
| topic | Information Theory 60Exx, 28A80, 94A34 |
| url | https://arxiv.org/abs/1606.00963 |