  We introduce the dispersion models with a regression structure to extend the
generalized linear models, the exponential family nonlinear models (Cordeiro
and Paula, 1989) and the proper dispersion models (J{\o}rgensen, 1997a). We
provide a matrix expression for the skewness of the maximum likelihood
estimators of the regression parameters in dispersion models. The formula is
suitable for computer implementation and can be applied for several important
submodels discussed in the literature. Expressions for the skewness of the
maximum likelihood estimators of the precision and dispersion parameters are
also derived. In particular, our results extend previous formulas obtained by
Cordeiro and Cordeiro (2001) and Cavalcanti et al. (2009). A simulation study
is perfomed to show the practice importance of our results.
