Quantization for the mixtures of uniform distributions on connected and disconnected line segments
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913980878946304 |
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| author | Barua, Asha Fernandez, Gustavo Gomez, Ashley Lopez, Ogla Roychowdhury, Mrinal Kanti |
| author_facet | Barua, Asha Fernandez, Gustavo Gomez, Ashley Lopez, Ogla Roychowdhury, Mrinal Kanti |
| contents | In this paper, we have studied various mixed distributions generated by two uniform distributions: first, where the supports are two connected line segments, and second, where the supports are two disconnected line segments. For these mixed distributions, we have determined the optimal sets of $n$-means and the corresponding $n$th quantization errors for all positive integers $n $. The methods developed in this paper can be applied more generally to investigate optimal quantization for any mixed distribution $P := pP_1 + (1 - p)P_2,$ where $P_1$ and $P_2$ are arbitrary probability distributions supported on either connected or disconnected line segments, and $(p, 1 - p)$ is any probability vector with $0 < p < 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_12664 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quantization for the mixtures of uniform distributions on connected and disconnected line segments Barua, Asha Fernandez, Gustavo Gomez, Ashley Lopez, Ogla Roychowdhury, Mrinal Kanti Probability 60E05, 94A34 In this paper, we have studied various mixed distributions generated by two uniform distributions: first, where the supports are two connected line segments, and second, where the supports are two disconnected line segments. For these mixed distributions, we have determined the optimal sets of $n$-means and the corresponding $n$th quantization errors for all positive integers $n $. The methods developed in this paper can be applied more generally to investigate optimal quantization for any mixed distribution $P := pP_1 + (1 - p)P_2,$ where $P_1$ and $P_2$ are arbitrary probability distributions supported on either connected or disconnected line segments, and $(p, 1 - p)$ is any probability vector with $0 < p < 1$. |
| title | Quantization for the mixtures of uniform distributions on connected and disconnected line segments |
| topic | Probability 60E05, 94A34 |
| url | https://arxiv.org/abs/2203.12664 |