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After a brief historical survey of parametric survival models, from actuarial, biomedical, demographical and engineering sources, this paper discusses the persistent reasons why parametric models still play an important role in exploratory statistical research. The phase-type models are advanced as a flexible family of latentclass models with interpretable components. These models are now supported by computational statistical methods that make numerical calculation of likelihoods anddoi:10.1007/s10985-013-9278-0 pmid:23963960 fatcat:cvbdsnhls5duvkmepbzb4yj2ci