The weibull-negative-binomialmodel under latent failure causes with randomized activation schemes.
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in this paper we propose the Weibull-NegativeBinomial(WNB) distribution under latent failure causes with randomized activation scheme. The proposed model is general by assuming a latent activation structure to explain the occurrence of an event of interest, where the number of competing causes are rnodeled by negative binomial distribution while the competitive causes may have different activation mechanisms, namely. first, random and last ones. Moreover, we derive some standard properties of the WNB distribution and discuss inference via the maximum likelihood approach. The WNB distribution generalizes various usual lifetime distributions, but particularly the extended Weibull—Geometric distribution introduced by Barreto-Souza et al. (2011), when the first activation scheme is considered, and the exponential—Poisson lifetime distribution proposed by Gancho et al. (2011), when the last activation scheme is considered. A misspecification simulation study comparing the proposed model in the presence of different activation schemes with the usual Weibull distribution is performed. Application of the proposed model in two sets of real data illustrates its flexibility.