  In general, the distribution of residuals cannot be obtained explicitly. We
give an asymptotic formula for the density of Pearson residuals in continuous
generalized linear models corrected to order $n^{-1}$, where $n$ is the sample
size. We define corrected Pearson residuals for these models that, to this
order of approximation, have exactly the same distribution of the true Pearson
residuals. Applications for important generalized linear models are provided
and simulation results for a gamma model illustrate the usefulness of the
corrected Pearson residuals.
