September 2023 Bivariate log-symmetric models: Distributional properties, parameter estimation and an application to public spending data
Roberto Vila, Narayanaswamy Balakrishnan, Helton Saulo, Ana Protazio
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Braz. J. Probab. Stat. 37(3): 619-642 (September 2023). DOI: 10.1214/23-BJPS584


The bivariate Gaussian distribution has been a key model for many developments in statistics. However, many real-world phenomena produce data that follow asymmetric distributions, and consequently bivariate normal model becomes inappropriate in such situations. Bidimensional log-symmetric models have attractive properties and can be considered as good alternatives in such situations. In this paper, we discuss bivariate log-symmetric distributions and their characterizations. We establish several distributional properties and also discuss the maximum likelihood estimation of 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.


This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES) (Finance Code 001). Roberto Vila and Helton Saulo gratefully acknowledge financial support from CNPq and FAP-DF, Brazil. The authors also express their sincere thanks to the editor and the anonymous reviewers for their comments and useful suggestions on an earlier version of this manuscript which lead to this improved version.


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Roberto Vila. Narayanaswamy Balakrishnan. Helton Saulo. Ana Protazio. "Bivariate log-symmetric models: Distributional properties, parameter estimation and an application to public spending data." Braz. J. Probab. Stat. 37 (3) 619 - 642, September 2023.


Received: 1 March 2023; Accepted: 1 September 2023; Published: September 2023
First available in Project Euclid: 22 November 2023

Digital Object Identifier: 10.1214/23-BJPS584

Keywords: Bivariate Log-symmetric Models , maximum likelihood method , Monte Carlo simulation , R software

Rights: Copyright © 2023 Brazilian Statistical Association


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Vol.37 • No. 3 • September 2023
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