This is the example from the Credibility chapter from Acted Book: May I know why the \sigma^2(\theta) = V_k*Var(X_k|\theta)? The Tables says Var(X) = alpha/lambda^2 which is V_k/(V_k/\theta)^2 only.
sigma^2(theta) is the Variance of severity while the Var(X) is the variance of claim per exposure (the more the expsoure the less the variance) If the above question rewords to distribution of the severity X_k|theta instead of average losses then sigma^2(theta) = Var(X|theta) right?
Per page 38 of Chapter 18, sigma^2(theta) is volume-adjusted variance of the claims ratio (as a function of theta (i)).
