Use the gamma distribution when a regression target is continuous, strictly positive, and right-skewed. Insurance claim amounts are a representative case: unusually large values create a long tail that should not simply be discarded as outliers. section 7.3.1
Unlike the Gaussian assumption, the gamma distribution is defined only for positive real values and can fit many target shapes. Its negative log-likelihood serves as a surrogate loss rather than a closed-form loss function; the gentler penalty for large positive-side errors supports fitting long-tailed data. section 7.3.1
Gamma regression connects the distributional assumption to a practical regression model:
- Use a linear model with a log-link function for continuous, positive, right-skewed targets. section 7.5
- Treat the gamma likelihood as appropriate when labels cannot take negative values. section 7.5
- Choose a different distribution when the target includes a substantial point mass at zero or combines count and positive-continuous behavior; a Tweedie model can combine Poisson and gamma components. section 7.4.1
Insurance claims and bike-sharing demand
For insurance, gamma regression matches continuous claim amounts with positive, long-tailed values. Bike-sharing demand illustrates the boundary: its count target has many zeros and a right-skewed positive tail, making a compound Poisson-gamma Tweedie model more suitable than gamma alone. section 7.3.1 section 7.4.1
Specialized gradient-boosting tools extend the generalized-linear-model intuition: LightGBM and XGBoost support log links and gamma objectives while allowing nonlinear models. section 7.5 section 7.4.1
