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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2204.12350 |
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| _version_ | 1866916654674345984 |
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| author | Zhang, Jialin Zhang, Zhiyi |
| author_facet | Zhang, Jialin Zhang, Zhiyi |
| contents | This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities developed from results of domains of attraction on countable alphabets -- theoretical evidence supports the identification of specific discrete distributional tail types through a sequence of plots. The approach discerns tail types by bench-marking against exponential, and three thicker-than-exponential families: near-exponential, sub-exponential, and power-law (zipf, Pareto). For tails thicker-than-exponential, the approach also provides point and interval estimates for some of the underlying distribution parameters. While primarily designed to streamline the selection of discrete parametric models for detailed statistical analysis, a supporting theorem enables the method's extension use to continuous data, stating that binning continuous data with a common width preserves the tail decay rate under certain conditions. Simulations are presented to demonstrate the method's performance across various scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_12350 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Non-parametric Approach to Inference about the Tail of a Continuous or a Discrete Distribution Zhang, Jialin Zhang, Zhiyi Applications Statistics Theory This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities developed from results of domains of attraction on countable alphabets -- theoretical evidence supports the identification of specific discrete distributional tail types through a sequence of plots. The approach discerns tail types by bench-marking against exponential, and three thicker-than-exponential families: near-exponential, sub-exponential, and power-law (zipf, Pareto). For tails thicker-than-exponential, the approach also provides point and interval estimates for some of the underlying distribution parameters. While primarily designed to streamline the selection of discrete parametric models for detailed statistical analysis, a supporting theorem enables the method's extension use to continuous data, stating that binning continuous data with a common width preserves the tail decay rate under certain conditions. Simulations are presented to demonstrate the method's performance across various scenarios. |
| title | A Non-parametric Approach to Inference about the Tail of a Continuous or a Discrete Distribution |
| topic | Applications Statistics Theory |
| url | https://arxiv.org/abs/2204.12350 |