I developed a family of probabilistic models to infer the extinction rate of prehistoric species using the fossil record. The problem’s challenge is that fossil record is highly censored data of the extinction rate, but it is also the best information. The data consisted of the oldest and most recent fossil for 36K species. The idea is to model the probability of observing the fossil’s age, conditional on being collected as a mixture of branching processes that represent fossilized phylogenetic trees. It is flexible enough to include more types of information other than the fossil record. We showed through simulations that our family of models produces similar data as the observed.