Family of distributions whose variance is proportional to a power of the mean, allowing direct modeling of pure premium despite the probability mass at zero from claim-free policies.
Modeling pure premium directly runs into an obstacle: 95% of policies have no claim, so the response variable is zero in most cases, which no classical continuous law represents. Standard practice works around it by modeling frequency with Poisson and average cost with gamma separately, then multiplying. The Tweedie family offers the one-pass alternative. It is characterized by a power parameter p such that variance equals the dispersion parameter times the mean to the power p, and for p strictly between one and two the resulting law is exactly a compound Poisson with gamma severities: it has a probability mass at zero and a continuous positive density beyond, which is the shape of pure premium. One model then suffices, which simplifies industrialization. The price is lost information: a Tweedie model does not say whether a rise in pure premium comes from frequency or from severity, a distinction that nonetheless calls for different actions, prevention on one side, claims handling on the other.
Homeowners rating, 2026 year, 240,000 policies of which 91% are claim free. A Tweedie model with p estimated at 1.62 returns an average pure premium of 168 EUR and a deviance within 1% of the frequency-severity approach. The lost decomposition proved costly six months later: the 9% rise seen on one segment came entirely from average cost, that is from materials prices, and not from a frequency drift the prevention team had started to address.
distribution de Tweedie, Tweedie distribution, compound Poisson-gamma, modèle de prime pure en une passe