In this paper, we consider a survival model of competing risks where the number of causes of failure is random, M, and only the minimum of the survival times due to various causes, Y = min(X1, X2, . . . , XM ), is observed. Considering the distribution of M as zero-truncated Poisson and the baseline distribution of X as generalized Lindley, a generalized Lindley-Poisson distribution is obtained. The structural properties of the proposed model are studied. The method of maximum likelihood is used to estimate the parameters of the proposed model. Simulation studies are carried out to study the performance of the estimators. Two real data sets are analyzed and it is shown that the proposed model fts better than some of the existing models.
