Table 1.
family | distributional parameters | mean (E[y]) variance (var[y]) | link function | delta method | lognormal approximation | trigamma function |
---|---|---|---|---|---|---|
quasi-Poisson (QP) | log | |||||
Poisson (when ω = 1) |
λ > 0 ω > 0 |
square-root | 0.25ω | — | ||
negative binomial (NB) | log | |||||
λ > 0 θ > 0 |
square-root | — | ||||
gamma | log | |||||
λ > 0 ν > 0 |
inverse (reciprocal) |
— | ||||
gamma (alternative parameterization) | log | |||||
ν > 0 κ > 0 |
inverse (reciprocal) |
— |