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General mathematical properties, regression and applications of the log-gamma-generated family

Author

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  • Gauss M. Cordeiro
  • Marcelo Bourguignon
  • Edwin M. M. Ortega
  • Thiago G. Ramires

Abstract

The construction of some wider families of continuous distributions obtained recently has attracted applied statisticians due to the analytical facilities available for easy computation of special functions in programming software. We study some general mathematical properties of the log-gamma-generated (LGG) family defined by Amini, MirMostafaee, and Ahmadi (2014). It generalizes the gamma-generated class pioneered by Ristić and Balakrishnan (2012). We present some of its special models and derive explicit expressions for the ordinary and incomplete moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves, Shannon entropy, Rényi entropy, reliability, and order statistics. Models in this family are compared with nested and non nested models. Further, we propose and study a new LGG family regression model. We demonstrate that the new regression model can be applied to censored data since it represents a parametric family of models and therefore can be used more effectively in the analysis of survival data. We prove that the proposed models can provide consistently better fits in some applications to real data sets.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:5:p:1050-1070
    DOI: 10.1080/03610926.2017.1316403
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    Cited by:

    1. 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.

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