Abstract In this article, we propose Bayesian methodology to obtain parameter estimates of the mixture of distributions belonging to the normal and biparametric Weibull families, modeling the mean and the variance parameters. Simulated studies and applications show the performance of the proposed models. Keywords: Bayesian inferenceMixture modelsNormal regressionWeibull regressionMathematics Subject Classification: 62J05 Acknowledgments Cepeda's work was supported by a grant from Universidad Nacional de Colombia. The authors would like to thank the reviewers for their comments, which were very helpful in the improvement of this article. Notes Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lsta.