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arXiv · 2403.00383

The Mollified (Discrete) Uniform Distribution and its Applications

Christian H. Weiß
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Abstract

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.

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Christian H. Weiß. 2024-03-01. The Mollified (Discrete) Uniform Distribution and its Applications. https://arxiv.org/abs/2403.00383

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