TY  - JOUR
T1  - Pareto Randomization of the Scaling Parameter for the Gaussian Distribution
AU  - Felgueiras, Miguel
AU  - Santos, Rui
AU  - Martins, Joao Paulo
PY  - 2021
DA  - December
Y2  - 2022
DO  - 10.53508/ijiam.1020679
JF  - International Journal of Informatics and Applied Mathematics
JO  - IJIAM
PB  - International Society of Academicians
WT  - DergiPark
SN  - 2667-6990
SP  - 43
EP  - 52
VL  - 4
IS  - 2
LA  - en
AB  - 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.
KW  - Pareto scale mixtures
KW  - heavy tail distributions
KW  - parameters estimation
KW  - ants direction
CR  - Jones, M., Pewsey, A.: A Family of Symmetric Distributions on the Circle. Journal of the American Statistical Association 100, 472, 1422--1428 (2005)
UR  - https://doi.org/10.53508/ijiam.1020679
L1  - https://dergipark.org.tr/en/download/article-file/2069867
ER  -