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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Marcelo Bourguignon & Manoel Santos-Neto & Mário Castro, 2021. "A new regression model for positive random variables with skewed and long tail," METRON, Springer;Sapienza Università di Roma, vol. 79(1), pages 33-55, April.
    • Handle: RePEc:spr:metron:v:79:y:2021:i:1:d:10.1007_s40300-021-00203-y
    DOI: 10.1007/s40300-021-00203-y
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    References listed on IDEAS

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    1. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    2. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 471-480, September.
    3. McDonald, James B. & Butler, Richard J., 1990. "Regression models for positive random variables," Journal of Econometrics, Elsevier, vol. 43(1-2), pages 227-251.
    4. Luca Bagnato & Antonio Punzo, 2013. "Finite mixtures of unimodal beta and gamma densities and the $$k$$ -bumps algorithm," Computational Statistics, Springer, vol. 28(4), pages 1571-1597, August.
    5. Masanobu Taniguchi & Junichi Hirukawa, 2012. "Generalized information criterion," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(2), pages 287-297, March.
    6. Stasinopoulos, D. Mikis & Rigby, Robert A., 2007. "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i07).
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    Cited by:

    1. Elisângela C. Biazatti & Gauss M. Cordeiro & Gabriela M. Rodrigues & Edwin M. M. Ortega & Luís H. de Santana, 2022. "A Weibull-Beta Prime Distribution to Model COVID-19 Data with the Presence of Covariates and Censored Data," Stats, MDPI, vol. 5(4), pages 1-15, November.
    2. Ahmad Abubakar Suleiman & Hanita Daud & Narinderjit Singh Sawaran Singh & Mahmod Othman & Aliyu Ismail Ishaq & Rajalingam Sokkalingam, 2023. "A Novel Odd Beta Prime-Logistic Distribution: Desirable Mathematical Properties and Applications to Engineering and Environmental Data," Sustainability, MDPI, vol. 15(13), pages 1-25, June.

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