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Modelling Asymmetric Data by Using the Log-Gamma-Normal Regression Model

Author

Listed:
  • Roger Tovar-Falón

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Monteria 230002, Colombia
    These authors contributed equally to this work.)

  • Guillermo Martínez-Flórez

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Monteria 230002, Colombia
    These authors contributed equally to this work.)

  • Heleno Bolfarine

    (Departamento de Estatística, Universidade de São Paulo, Sao Paulo 05508-090, Brazil
    These authors contributed equally to this work.)

Abstract

In this paper, we propose a linear regression model in which the error term follows a log-gamma-normal (LGN) distribution. The assumption of LGN distribution gives flexibility to accommodate skew forms to the left and to the right. Kurtosis greater or smaller than the normal model can also be accommodated. The regression model for censored asymmetric data is also considered (censored LGN model). Parameter estimation is implemented using the maximum likelihood approach and a small simulation study is conducted to evaluate parameter recovery. The main conclusion is that the approach is very much satisfactory for moderate and large sample sizes. Results for two applications of the proposed model to real datasets are provided for illustrative purposes.

Suggested Citation

  • Roger Tovar-Falón & Guillermo Martínez-Flórez & Heleno Bolfarine, 2022. "Modelling Asymmetric Data by Using the Log-Gamma-Normal Regression Model," Mathematics, MDPI, vol. 10(7), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1199-:d:787991
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    References listed on IDEAS

    as
    1. Rameshwar Gupta & Ramesh Gupta, 2008. "Analyzing skewed data by power normal model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 197-210, May.
    2. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    3. Hung-Ping Tung & Sheng-Tsaing Tseng & Nan-Jung Hsu & Yi-Ting Hou, 2022. "A generalized pH acceleration model of nano-sol products and the effects of model misspecification on shelf-life prediction," IISE Transactions, Taylor & Francis Journals, vol. 54(5), pages 496-504, May.
    4. Gauss M. Cordeiro & Marcelo Bourguignon & Edwin M. M. Ortega & Thiago G. Ramires, 2018. "General mathematical properties, regression and applications of the log-gamma-generated family," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(5), pages 1050-1070, March.
    5. Ortega, Edwin M. M. & Bolfarine, Heleno & Paula, Gilberto A., 2003. "Influence diagnostics in generalized log-gamma regression models," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 165-186, February.
    6. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    7. Daowen Zhang & Marie Davidian, 2001. "Linear Mixed Models with Flexible Distributions of Random Effects for Longitudinal Data," Biometrics, The International Biometric Society, vol. 57(3), pages 795-802, September.
    8. Arthur Pewsey & Héctor Gómez & Heleno Bolfarine, 2012. "Likelihood-based inference for power distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 775-789, December.
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