Pareto Randomization of the Scaling Parameter for the Gaussian Distribution

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

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