Pareto Randomization of the Scaling Parameter for the Gaussian Distribution

Year 2021, , 43 - 52, 31.12.2021

Miguel Felgueiras Rui Santos Joao Paulo Martins

https://doi.org/10.53508/ijiam.1020679

Abstract

Gaussian distribution is a common choice when dealing with symmetric data. However, other alternatives must be considered in applications with high tail-weight. One option is the randomization of the scale parameter for the Gaussian distribution, enabling a more flexible model for the tails albeit maintaining symmetry. Although any positive random variable can be used as a random scale parameter, Pareto distribution is a suitable choice in order to increase variance and tail-weight. Therefore, the aim of this work is to study the Pareto randomization of the scale parameter for symmetric distributions, in particular for the Gaussian distribution. Estimation problem is tackled and a simulation study is discussed. Finally, an application concerning the directions chosen by ants after a stimulus is provided. The results reveal that the proposed methodology works well both on simulated and real data.

Keywords

Pareto scale mixtures, heavy tail distributions, parameters estimation, ants direction

Supporting Institution

Fundação para a Ciência e Tecnologia

Project Number

UIDB/00006/2020

References

• Jones, M., Pewsey, A.: A Family of Symmetric Distributions on the Circle. Journal of the American Statistical Association 100, 472, 1422--1428 (2005)