On Robust Regression: A Model with Weibull Error Term

A regression model based on the Weibull error distribution has been developed to address the challenges of modeling skewed response variables commonly encountered in environmental and life sciences data. By introducing a location parameter to the standard Weibull distribution, the model accommodates asymmetry and heavy tails that linear normal-based regression often fails to capture. Parameter estimation was carried out using the Newton–Raphson algorithm, implemented in the R program WeiReg. Model comparison based on the Akaike Information Criterion (AIC) demonstrates that the Weibull regression provides a substantially better fit than the linear regression model when applied to wind speed data from Christmas Island, Australia. These findings highlight the relevance of flexible error structures in regression modeling and underscore the practical value of the Weibull approach for analyzing environmental data.