Exponential Family and Link Functions

Free SOA Exam SRM (Statistics for Risk Modeling) lesson in Linear Models. 19 min read, ~2,783 words.

A distribution is in the exponential family if. Members: normal, binomial, Poisson, gamma, inverse Gaussian, and negative binomial (fixed dispersion). is the canonical (natural) parameter; the dispersion;;. The link connects linear predictor to mean:. The canonical link sets, so the linear predictor equals the natural parameter. Canonical links by family...