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

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.