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Generalized Beta Weibull Linear Model: Estimation, Diagnostic Tools and Residual Analysis

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Abstract

We propose a new regression model based on the concepts of generalized linear models (GLMs), assuming the beta Weibull distribution. Similar to GLMs, the proposed model is called the generalized beta Weibull linear model (GBWLM). The maximum likelihood estimation of the parameters assuming the Newton–Raphson algorithm is discussed. The local influence methodology regarding three perturbation schemes is developed for the GBWLM. To check the model assumptions, detect atypical observations and verify the goodness of fit of the regression model, residuals based on the quantile function are proposed and a Monte Carlo simulation study is performed to construct simulated envelopes.

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Acknowledgements

We are very grateful to a referee and an associate editor for helpful comments that considerably improved the paper. We gratefully acknowledge the financial support from CAPES and CNPq Brazil.

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Authors and Affiliations

  1. Department of Statistics, State University of Londrina, Rodovia Celso Garcia Cid, Pr 445 Km 380, Londrina, PR, Brazil

    Tiago V. F. Santana

  2. Department of Mathematical Sciences, University of São Paulo, Av. Pádua Dias 11, Piracicaba, SP, 13418-900, Brazil

    Edwin M. M. Ortega

  3. Department of Statistics, University Federal of Pernambuco, Cidade Universitária, Recife, PE, 50740-540, Brazil

    Gauss M. Cordeiro

Authors
  1. Tiago V. F. Santana
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  2. Edwin M. M. Ortega
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  3. Gauss M. Cordeiro
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Correspondence to Tiago V. F. Santana.

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Santana, T.V.F., Ortega, E.M.M. & Cordeiro, G.M. Generalized Beta Weibull Linear Model: Estimation, Diagnostic Tools and Residual Analysis. J Stat Theory Pract 13, 16 (2019). https://doi.org/10.1007/s42519-018-0022-7

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  • DOI: https://doi.org/10.1007/s42519-018-0022-7

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