An alternative to the usual residual (see regression diagnostics) which Anscombe proposed in 1953 for cases where the random errors in a general regression model do not have a normal distribution. The idea is to produce quantities that do have near-normal distributions, and the form for the residual depends upon the error distribution assumed.
In the case of a Poisson distribution, an Anscombe residual is given by
where y and ŷ are, respectively, observed and fitted values. In the case of a gamma distribution the formula becomes
and in the case of an inverse normal distribution the formula is
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