Bivariate log-symmetric models: distributional properties, parameter estimation and an application to fatigue data analysis

Abstract

The bivariate Gaussian distribution has been a key model for many developments in statistics. However, many real-world phenomena generate data that follow asymmetric distributions, and consequently bivariate normal model is inappropriate in such situations. Bidimensional log-symmetric models have attractive properties and can be considered as good alternatives in these cases. In this paper, we discuss bivariate log-symmetric distributions and their characterizations. We establish several distributional properties and obtain the maximum likelihood estimators of the model parameters. A Monte Carlo simulation study is performed for examining the performance of the developed parameter estimation method. A real data set is finally analyzed to illustrate the proposed model and the associated inferential method.