The predominant analytic approach in epidemiological studies is linear mean regression. In linear regression, it is assumed that the covariates aﬀect only the mean of the response distribution and no other aspect, such as variance or skewness. While this approach is computationally eﬃcient and easy to interpret, it is insuﬃcient in many cases. For example, linear regression can miss subtle relationships such as covariate eﬀects on the variance or the likelihood of extreme events. Also, linear regression is known to be sensitive to outlying observations.