C4. Exponential family
What is an exponential family? Identify its natural parameter and statistic.
Worked answer (click to show)
Definitions/notation. An exponential family has density or mass function f(x\mid\theta)=b(x)\exp\{c(\theta)^\top T(x)\}/a(\theta), where c(\theta) is the natural parameter, T(x) the natural statistic, b(x) a parameter-free base factor and a(\theta) the normalising function. In the regular form used here, the support is independent of \theta.