The Weibull negative binomial distribution (BNW) is proposed which generalizes the Weibull geometric distribution (WG) is introduced by Barreto-Souza et al. (2010). Furthermore, we propose a model for survival data with cure fraction, which includes as special cases the traditional models of survival with cure fraction of Berkson & Gage (1952) and Chen et al. (1999). The new propose survival's model with cure fraction assume an activation of latent structure in explaining the occurrence of an event of interest. The proposal is based on negative binomial distribution for the number of causes of occurrence of event of interest in statistics and order of activation times to explain the latent time before the event of interest. The objective of this project is to study characteristics of the proposed models, as well as develop procedures and diagnostic inferences from a frequentist and Bayesian perspective.
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