This article aims to provide rigorous and convenient statistical models for dealing with high-variability phenomena. The presence of discrepance in variance represents a substantial issue when it is not possible to reduce variability before analysing the data, leading to the possibility to estimate an inadequate model. In this paper, the application of Generalized Additive Model for Location, Scale and Shape (GAMLSS) and the use of finite mixture model for GAMLSS will be proposed as a solution to the problem of overdispersion. An application to Liver fibrosis data is illustrated in order to identify potential risk factors for patients, which could determine the presence of the disease but also its levels of severity.
Keywords: liver diseases; mixture models; residual analysis; worm plot.