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Tests of separate families of hypotheses were initially considered by Cox (1961,1962). In this paper we examine the Fully Bayesian Signicance Test, FBST, for discriminating between the lognormal andWeibull models whose families of distributions are separate. Here, we analyze this problem in the context of linear mixture models. The FBST procedure is used for testing the hypotheses on the mixture weights in order to
calculate the evidence measure in favor of each model. In this work, the density functions of the mixture components are reparametrized in terms of the common parameters, the mean and the variance of the population, since the comparison between the models is based on the same dataset, that is, on the same population. In order to evaluate the performance of the proposed method, some numerical results based on simulations of sample points are given. In these simulations, the results of FBST are compared with those of the Cox test. Two application examples illustrating the procedures for uncensored data set are also presented.
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