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

TL;DR

This paper introduces bivariate log-symmetric models as flexible alternatives to the bivariate normal distribution for asymmetric data, detailing their properties, estimation methods, and application to fatigue data analysis.

Contribution

It characterizes bivariate log-symmetric distributions, derives their properties, and develops maximum likelihood estimators, with validation through simulations and real data application.

Findings

Distributional properties established

Maximum likelihood estimators derived and validated

Model successfully applied to fatigue data

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.