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Semi-Markov models, independently introduced by Lévy (1954), Smith (1955) and Takacs (1954), are a generalization of the well-known Markov models. For semi-Markov models, sojourn times can be arbitrarily distributed, while sojourn times of Markov models are constrained to be exponentially distributed (in continuous time) or geometrically distributed (in discrete time). The aim of this paper is to present the R package SMM, devoted to the simulation and estimation of discrete-time multi-state semi-Markov and Markov models. For the semi-Markov case we have considered: parametric and non-parametric estimation; with and without censoring at the beginning and/or at the end of sample paths; one or several independent sample paths. Several discrete-time distributions are considered for the parametric estimation of sojourn time distributions of semi-Markov chains: Uniform, Geometric, Poisson, Discrete Weibull and Binomial Negative.

SMM: An R Package for Estimation and Simulation of Discrete-time semi-Markov Models