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We propose two new regressions based on the generalized odd log-logistic log-normal distribution allowing for positive and negative skewness to model bimodal data. The first one is the parametric regression and the second one is an additive partial linear regression. The new regressions aim to estimate the linear and non-linear effects of covariables on the response variable and generalize some existing regressions in the literature. For both cases, the model parameters are estimated by the methods of maximum likelihood and maximum penalized likelihood. In particular, a model check based on the quantile residuals is used to select the appropriate covariables. We reanalyze two data sets, one for each proposed regression.

The parametric and additive partial linear regressions based on the generalized odd log-logistic log-normal distribution