On some generalization of the normal distribution

Krzysztof Zajkowski

Published 2021-07-31Version 1

In this paper we propose some new generalization of the normal distribution. We will call it the $\alpha$- normal (Gaussian) distribution. For $\alpha=2$ it becomes the standard normal distribution. We show expression for moments and the differential entropy. We also calculate the (exponential) Orlicz norm of the standard $\alpha$-normal random variables.