Nearly Gaussian random variables and application to meteorology

TL;DR

This paper explores nearly Gaussian random variables and their transformations, demonstrating their application in modeling temperature forecast errors in meteorology.

Contribution

It introduces a specific power transformation for nearly Gaussian variables, enhancing error modeling in meteorological temperature forecasts.

Findings

The transformation makes temperature forecast errors approximately Gaussian.

Application of the transformation improves error modeling accuracy.

Provides a mathematical framework for nearly Gaussian variables.

Abstract

We consider a nearly Gaussian random variable $X$ (see \cite{Lefebvre}) that, after a power transformation, the variable $X^c$ where $c=\{(2k+1)/(2j+1)\}$, $k,j=\{0,1,\dots\}$, is approximately Gaussian. This transformation is useful to model errors in temperature forecasts.