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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.00383 |
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| _version_ | 1866913589305016320 |
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| author | Weiß, Christian H. |
| author_facet | Weiß, Christian H. |
| contents | The mollified uniform distribution is rediscovered, which constitutes a ``soft'' version of the continuous uniform distribution. Important stochastic properties are presented and used to demonstrate potential fields of applications. For example, it constitutes a model covering platykurtic, mesokurtic and leptokurtic shapes. Its cumulative distribution function may also serve as the soft-clipping response function for defining generalized linear models with approximately linear dependence. Furthermore, it might be considered for teaching, as an appealing example for the convolution of random variables. Finally, a discrete type of mollified uniform distribution is briefly discussed as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00383 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Mollified (Discrete) Uniform Distribution and its Applications Weiß, Christian H. Methodology The mollified uniform distribution is rediscovered, which constitutes a ``soft'' version of the continuous uniform distribution. Important stochastic properties are presented and used to demonstrate potential fields of applications. For example, it constitutes a model covering platykurtic, mesokurtic and leptokurtic shapes. Its cumulative distribution function may also serve as the soft-clipping response function for defining generalized linear models with approximately linear dependence. Furthermore, it might be considered for teaching, as an appealing example for the convolution of random variables. Finally, a discrete type of mollified uniform distribution is briefly discussed as well. |
| title | The Mollified (Discrete) Uniform Distribution and its Applications |
| topic | Methodology |
| url | https://arxiv.org/abs/2403.00383 |