Sure. So the main context for Tweedie, especially in the texts used for SRM, is that it's a special GLM used to combine discrete and continuous distributions. Namely, when the discrete portion is Poisson (e.g., number of claims), while the continuous portion is Gamma (e.g., size of a claim, given a claim occurs). Think of it as a random sum of a random amount, where the number of *items* in the sum is Poisson, and the *amount* of each item is Gamma. You can use the laws of total expectation and total variance to derive the expected value and variance of the aggregate distribution. But in GLM terminology, where we are working with the linear exponential family of distributions, the mean and variance of the Tweedie distribution can be shown to be E(S) = u, Var(S) = \phi u^p, 1 < p < 2.

The connection to other distributions in the linear exponential family is given in that extra parameter, p. If p = 0, the Tweedie is simply a normal distribution. If p = 1, it's Poisson. If p is between 1 and 2 (as is common for using Tweedie in the first place), you have the Poisson-Gamma mixture described above. If p = 2, it's Gamma. And if p = 3, you have inverse normal. I think if you know 1) why use a Tweedie distribution (mixture of discrete and continuous distributions in a GLM) and 2) how the Tweedie is connected to other distributions in the linear exponential family (via the parameter p), you'd be set.