Bivariate log-symmetric models: Theoretical properties and parameter estimation

The bivariate Gaussian distribution has been the basis of probability and statistics for many years. Nonetheless, this distribution faces some problems, mainly due to the fact that many real-world phenomena generate data that follow asymmetric distributions. Bidimensional log-symmetric models have attractive properties and can be considered as good alternatives to solve this problem. In this paper, we discuss bivariate log-symmetric distributions and their characterizations. We derive several statistical properties and obtain the maximum likelihood estimators of the model parameters. A Monte Carlo simulation study is performed to evaluate the performance of the parameter estimation method. A real data set is finally analyzed to illustrate the proposed approach.