A new regression model for positive random variables with skewed and long tail

Marcelo Bourguignon (), Manoel Santos-Neto and Mário Castro
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Marcelo Bourguignon: Universidade Federal do Rio Grande do Norte
Manoel Santos-Neto: Universidade Federal de Campina Grande
Mário Castro: Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação

METRON, 2021, vol. 79, issue 1, No 2, 33-55

Abstract: Abstract In this paper, we propose a regression model where the response variable is beta prime distributed using a new parameterization of this distribution that is indexed by mean and precision parameters. The proposed regression model is useful for situations where the variable of interest is continuous and restricted to the positive real line and is related to other variables through the mean and precision parameters. The variance function of the proposed model has a quadratic form. In addition, the beta prime model has properties that its competitor distributions of the exponential family do not have. Estimation is performed by maximum likelihood. Furthermore, we discuss residuals and influence diagnostic tools. Finally, we also carry out an application to real data that demonstrates the usefulness of the proposed model.

Keywords: Beta prime distribution; Generalized beta of the second kind; Local influence; Maximum likelihood estimator; Regression models; Residuals; Variance function (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s40300-021-00203-y

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