The mollified (discrete) uniform distribution and its applications

Weiß, Christian H.

doi:10.1002/wics.70016

The mollified (discrete) uniform distribution and its applications

Publication date

2025-02-03

Document type

Forschungsartikel

Author

Weiß, Christian H.

Organisational unit

Quantitative Methoden der Wirtschaftswissenschaften

DOI

10.1002/wics.70016

URI

https://openhsu.ub.hsu-hh.de/handle/10.24405/20195

Scopus ID

2-s2.0-85216930794

Publisher

Wiley-Blackwell

Series or journal

Wiley Interdisciplinary Reviews Computational Statistics

ISSN

1939-0068

Periodical volume

17

Periodical issue

1

Article ID

e70016

Peer-reviewed

✅

Part of the university bibliography

✅

Language

English

Keyword

convolution

discrete uniform distribution

Kurtosis

Mollified uniform distribution

Soft-clipping regression

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.

Description

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Version

Published version

Access right on openHSU

Metadata only access

Open Access Funding

Wiley (DEAL)