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We introduce the dispersion models with a regression structure to extend thegeneralized linear models, the exponential family nonlinear models (Cordeiroand Paula, 1989) and the proper dispersion models (J{\o}rgensen, 1997a). Weprovide a matrix expression for the skewness of the maximum likelihoodestimators of the regression parameters in dispersion models. The formula issuitable for computer implementation and can be applied for several importantsubmodels discussed in the literature. Expressions for the skewness of themaximum likelihood estimators of the precision and dispersion parameters arealso derived. In particular, our results extend previous formulas obtained byCordeiro and Cordeiro (2001) and Cavalcanti et al. (2009). A simulation studyis perfomed to show the practice importance of our results.

Skewness of maximum likelihood estimators in dispersion models