ABSTRACT. We introduce the Weibull distributions in presence of cure fraction, censored data and covariates. Two models are explored in this paper: mixture and non-mixture models. Inferences for the proposed models are obtained under the Bayesian approach, using standard MCMC (Markov Chain Monte Carlo) methods. An illustration of the proposed methodology is given considering a lifetime data set.

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ABSTRACT. Recently, [12] introduced a generalization of a one parameter Lindley distribution and named it as a weighted Lindley distribution. Considering this new introduced weighted Lindley distribution, we propose a reparametrization on the shape parameter leading it to be orthogonal to the other shape parameter. In this alternative parametrization, we get a direct interpretation for this transformed parameter which is the mean survival time. For illustrative purposes, the weighted Lindley distribution on the new parametrization is applied on two real data sets. The one parameter Lindley distribution and its generalized form are fitted for the considered data sets.

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