= Deviance residual
{title2=$r_i^D=\operatorname{sign}(y_i-\widehat\mu_i)\sqrt{d_i}$}
A deviance residual is the signed square root of an observation's contribution $d_i$ to fitted-model deviance. For a <Poisson regression>, $d_i=2[y_i\log(y_i/\widehat\mu_i)-(y_i-\widehat\mu_i)]$, with $0\log0=0$. Its squared sum is the <Poisson deviance>. Leverage and estimated dispersion can further standardize these residuals; a normal <quantile-quantile plot> is a diagnostic approximation, not a requirement that count errors have a <normal distribution>.
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