Generalized regression models when responses follow family of flexible distributions

Abstract: During the recent two decades, several frameworks were proposed to develop generalized flexible statistical distributions for fitting highly skewed, leptokurtic or platykurtic data distributions. Some noticeable frameworks include (a) skewed symmetric distributions, (b) adding one additional parameter to existing distributions (c) Beta-generated family and its extensions, including T-R{Z} family and (d) transmuted family. Some of the generalized distributions have been applied to fit regression models by assuming the responses following some flexible distributions. In this presentation, a framework for modeling the location parameter of response variables following the T-R{Z} family of distributions will be presented. Three types of generalized regression models will be presented, depending on the types of T-R{Z} family of distributions. A generalized distribution based on the T-R{Z} framework, namely, Kumaraswamy-Dagum (Kum-D) distribution is derived, along with some properties. A generalize regression model with the response assumed to the Kum-D is derived and applied to model the physical health condition on a list of covariates using the survey data collected in Albert, Canada.