Family of bivariate distributions on the unit square: theoretical properties and applications

Abstract

We introduce the bivariate unit-log-symmetric model based on the bivariate log-symmetric distribution (BLS) defined in Vila et al. [25] 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 marginal moments. Maximum likelihood estimation method is discussed and examined through Monte Carlo simulation. Finally, the proposed model is used to analyze some soccer data sets.

Keywords:

• Bivariate unit-log-symmetric distribution
• bivariate log-symmetric distribution
• MCMC
• proportion data
• soccer data
• maximum likelihood estimation

2010 Mathematics Subject Classifications:

• 60E05
• 62Exx
• 62Fxx

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Roberto Vila and Helton Saulo gratefully acknowledge financial support from CNPq, CAPES and FAPDF, Brazil.