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New class of Johnson S B distributions and its associated regression model for rates and proportions
Author(s) -
Lemonte Artur J.,
Bazán Jorge L.
Publication year - 2016
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201500030
Subject(s) - mathematics , univariate , regression analysis , leverage (statistics) , statistics , class (philosophy) , bounded function , regression , regression diagnostic , econometrics , polynomial regression , computer science , multivariate statistics , artificial intelligence , mathematical analysis
By starting from the Johnson S B distribution pioneered by Johnson ([Johnson, N. L., 1949]), we propose a broad class of distributions with bounded support on the basis of the symmetric family of distributions. The new class of distributions provides a rich source of alternative distributions for analyzing univariate bounded data. A comprehensive account of the mathematical properties of the new family is provided. We briefly discuss estimation of the model parameters of the new class of distributions based on two estimation methods. Additionally, a new regression model is introduced by considering the distribution proposed in this article, which is useful for situations where the response is restricted to the standard unit interval and the regression structure involves regressors and unknown parameters. The regression model allows to model both location and dispersion effects. We define two residuals for the proposed regression model to assess departures from model assumptions as well as to detect outlying observations, and discuss some influence methods such as the local influence and generalized leverage. Finally, an application to real data is presented to show the usefulness of the new regression model.