We introduce the Student's t-distribution as a robust alternative to the Gaussian distribution. It turns out that the Student's t-distribution can also be thought of as a continuous mixture. In this case we have:

Notice this is similar to the previous expression for the negative-binomial, except here we have a Normal distribution with the parameters and  and the  distribution with the parameter from which we sample the values of is the parameter known as a degree of freedom, or as we prefer to call it, the normality parameter. The parameter , as well as  for the beta-binomial, is the equivalent of the  latent variable for finite mixture models. For some finite mixture models, it is also possible to marginalize the distribution respect to the latent variable before doing inference, winch may lead to an easier to sample model, as we already saw with the marginalized mixture model example.