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Tests of separate families of hypotheses were initially considered by Cox(1961,1962) In this work, the Fully Bayesian Significance Test, FBST, isevaluated for discriminating between the lognormal, gamma and Weibull modelswhose families of distributions are separate. Considering a linear mixturemodel including all candidate distributions, the FBST tests the hypotheses onthe mixture weights in order to calculate the evidence measure in favor of eachone. Additionally, the density functions of the mixture components arereparametrized in terms of the common parameters, the mean and the variance ofthe population, since the comparison between the models is based on the samedataset, i.e, on the same population. Reparametrizing the models in terms ofthe common parameters also allows one to reduce the number of the parameters tobe estimated. In order to evaluate the performance of the procedure, somenumerical results based on simulated sample points are given. In thesesimulations, the results of FBST are compared with those of the Cox test. Twoapplications examples illustrating the procedure for uncensored dataset arealso presented.  Keywords: Model choice; Separate Models; Mixture model; Significance test;FBST; Cox Test

Model choice in separate families: A comparison between the FBST and the Cox test