PhaseTypeR: phase-type distributions in R with reward transformations and a view towards population genetics

Abstract Phase-type distributions are a general class of models that are traditionally used in actuarial sciences and queuing theory, and more recently in population genetics. A phase-type distributed random variable is the time to absorption in a discrete or continuous time Markov chain on a finite state space with an absorbing state. The R package PhaseTypeR contains all the key functions—mean, (co)variance, probability density function, cumulative distribution function, quantile function, random sampling and reward transformations—for both continuous (PH) and discrete (DPH) phase-type distributions. Additionally, we have also implemented the multivariate continuous case (MPH) and the multivariate discrete case (MDPH). We illustrate the usage of PhaseTypeR in simple examples from population genetics (e.g. the time until the most recent common ancestor or the total number of mutations in an alignment of homologous DNA sequences), and we demonstrate the power of PhaseTypeR in more involved applications from population genetics, such as the coalescent with recombination and the structured coalescent. The multivariate distributions and ability to reward-transform are particularly important in population genetics, and a unique feature of PhaseTypeR.