Bivariate beta-generated distributions with applications to well-being data

José Sarabia,Vanesa Jordá,Faustino Prieto

doi:10.1186/2195-5832-1-15

José Sarabia, Vanesa Jordá + Show 1 more

Open Access

https://doi.org/10.1186/2195-5832-1-15

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Abstract

The class of beta-generated distributions (Commun. Stat. Theory Methods 31:497–512, 2002; TEST 13:1–43, 2004) has received a lot of attention in the last years. In this paper, three new classes of bivariate beta-generated distributions are proposed. These classes are constructed using three different definitions of bivariate distributions with classical beta marginals and different covariance structures. We work with the bivariate beta distributions proposed in (J. Educ. Stat. 7:271–294, 1982; Metrika 54:215–231, 2001; Stat. Probability Lett. 62:407–412, 2003) for the first proposal, in (Stat. Methods Appl. 18: 465–481, 2009) for the second proposal and (J. Multivariate Anal. 102:1194–1202, 2011) for the third one. In each of these three classes, the main properties are studied. Some specific bivariate beta-generated distributions are studied. Finally, some empirical applications with well-being data are presented. 62E15; 60E05

Highlights

In the recent statistical literature several methodologies of constructing bivariate and multivariate distributions based on marginal and conditional distributions have been proposed; see the works by Arnold et al (1999; 2001), Kotz et al (2000), Sarabia and Gómez-Déniz (2008) and Balakrishnan and Lai (2009) among others.An important field of research focuses on the study of new classes of univariate distributions which contain the classical proposals, allowing for more flexibility in fitting data
We work with the bivariate beta distributions proposed by Libby and Novick (1982), Jones (2001) and Olkin and Liu (2003) for the first proposal, El-Bassiouny and Jones (2009) for the second proposal and Arnold and Ng (2011) for the third one
3 Three classes of bivariate beta-generated distributions we introduce three new classes of bivariate BG distributions

Summary

Introduction

In the recent statistical literature several methodologies of constructing bivariate and multivariate distributions based on marginal and conditional distributions have been proposed; see the works by Arnold et al (1999; 2001), Kotz et al (2000), Sarabia and Gómez-Déniz (2008) and Balakrishnan and Lai (2009) among others. An important field of research focuses on the study of new classes of univariate distributions which contain the classical proposals, allowing for more flexibility in fitting data. In this sense, the class of beta-generated (BG) distributions (Eugene et al 2002; Jones 2004) has received an increasing amount of attention in recent years. We work with the bivariate beta distributions proposed by Libby and Novick (1982), Jones (2001) and Olkin and Liu (2003) for the first proposal, El-Bassiouny and Jones (2009) for the second proposal and Arnold and Ng (2011) for the third one For each of these three classes, the main properties are obtained.

Some univariate and multivariate beta-generated distributions

Estimation

Findings

Conclusions