Bivariate distributions on the unit square: Theoretical properties and applications

TL;DR

This paper introduces a flexible bivariate distribution model on the unit square, explores its mathematical properties, discusses estimation methods, and applies it to analyze soccer data.

Contribution

It presents a new bivariate log-symmetric distribution model with detailed theoretical properties and practical estimation techniques.

Findings

Model exhibits desirable stochastic properties.

Maximum likelihood estimation is effective via simulations.

Application to soccer data demonstrates practical utility.

Abstract

We introduce the bivariate unit-log-symmetric model based on the bivariate log-symmetric distribution (BLS) defined in [Vila et al., 2022, Bivariate Log-symmetric Models: Theoretical Properties and Parameter Estimation. Avaliable at arXiv:2211.13839] as a flexible family of bivariate distributions over the unit square. We then study its mathematical properties such as stochastic representations, quantiles, conditional distributions, independence of the marginal distributions and moments. Maximum likelihood estimation method is discussed and examined through Monte Carlo simulation. Finally, the proposed model is used to analyze soccer data.