On different characterizations of a normal distribution

Bachelor thesis (2018)

Authors

H. van Wiechen Electrical Engineering, Mathematics and Computer Science

Contributors

M.C. Veraar (mentor)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2018 Hidde van Wiechen
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Published Date

31-08-2018

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

The normal distribution is a very important distribution in probability theory and statisticsand has a lot of unique properties and characterizations. In this report we look at the proof of two of these characterizations and create counterparts of a normal distribution on abstract spaces, such as vector spaces and groups, which we shall call Gaussians. When we look at R^d, all these Gaussians coincide, along with a Gaussian vector in the normal sense, called multivariate normal. Furthermore, for one Gaussian we prove that it has exponential integrability properties.

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