Quantization for the mixtures of overlap probability distributions
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913980919840768 |
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| author | Barua, Asha Chavera, Angelina Djordjevic, Ivan Manzano, Valerie Quintero, Sergio Soto Roychowdhury, Mrinal Kanti Tejeda, Hilda |
| author_facet | Barua, Asha Chavera, Angelina Djordjevic, Ivan Manzano, Valerie Quintero, Sergio Soto Roychowdhury, Mrinal Kanti Tejeda, Hilda |
| contents | Optimal quantization for mixed distributions has emerged as a compelling area of study. In this work, we have focused on a mixed distribution formed from two uniform distributions with partially overlapping supports. For this class of distributions, we have examined the structure of optimal sets of $n$-means and the corresponding $n$th quantization errors for all positive integers $n$. Initially, we explicitly determined the optimal sets and quantization errors for $1 \leq n \leq 6$. Subsequently, we established several key lemmas and propositions and proposed an algorithm that facilitates the computation of optimal $n$-means and quantization errors for all $n \geq 5$. Numerical results are also presented to illustrate the application of the algorithm in deriving these quantities. The findings of this study offer valuable insight and serve as a foundation for further research on quantization in the context of mixed distributions with overlapping supports. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_14152 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quantization for the mixtures of overlap probability distributions Barua, Asha Chavera, Angelina Djordjevic, Ivan Manzano, Valerie Quintero, Sergio Soto Roychowdhury, Mrinal Kanti Tejeda, Hilda Probability 60E05, 94A34 Optimal quantization for mixed distributions has emerged as a compelling area of study. In this work, we have focused on a mixed distribution formed from two uniform distributions with partially overlapping supports. For this class of distributions, we have examined the structure of optimal sets of $n$-means and the corresponding $n$th quantization errors for all positive integers $n$. Initially, we explicitly determined the optimal sets and quantization errors for $1 \leq n \leq 6$. Subsequently, we established several key lemmas and propositions and proposed an algorithm that facilitates the computation of optimal $n$-means and quantization errors for all $n \geq 5$. Numerical results are also presented to illustrate the application of the algorithm in deriving these quantities. The findings of this study offer valuable insight and serve as a foundation for further research on quantization in the context of mixed distributions with overlapping supports. |
| title | Quantization for the mixtures of overlap probability distributions |
| topic | Probability 60E05, 94A34 |
| url | https://arxiv.org/abs/2207.14152 |