Generalized Weibull Linear Models

Abstract

For the first time, a new class of generalized Weibull linear models is introduced to be competitive to the well-known generalized (gamma and inverse Gaussian) linear models which are adequate for the analysis of positive continuous data. The proposed models have a constant coefficient of variation for all observations similar to the gamma models and may be suitable for a wide range of practical applications in various fields such as biology, medicine, engineering, and economics, among others. We derive a joint iterative algorithm for estimating the mean and dispersion parameters. We obtain closed form expressions in matrix notation for the second-order biases of the maximum likelihood estimates of the model parameters and define bias corrected estimates. The corrected estimates are easily obtained as vectors of regression coefficients in suitable weighted linear regressions. The practical use of the new class of models is illustrated in one application to a lung cancer data set.

Keywords:

• Bias correction
• Dispersion parameter
• Information matrix
• Link function
• Orthogonal parameters
• Weibull regression model

Mathematics Subject Classification:

• 62F03
• 62F05

Acknowledgment

We gratefully acknowledge the partial financial support from the Brazilian agencies: CNPq and CAPES. We thank a referee for suggestions that improved the article.