Saddlepoint approximations to the moments of multitype age-dependent branching processes, with applications

This article proposes saddlepoint approximations to the expectation and variance-covariance function of multitype age-dependent branching processes. The proposed approximations are found accurate, easy to implement, and much faster to compute than by simulating the process. Multiple applications are presented, including the analyses of clonal data on the generation of oligodendrocytes from their immediate progenitor cells, and on the proliferation of Hela cells. New estimators are also constructed to analyze clonal data. The proposed methods are finally used to approximate the distribution of the generation, which has recently found several applications in cell biology.