In this thesis, we consider a competing risks scenario wherein lifetimes are potentially right censored. Instead of considering all the patients to be at risk to the event of interest, we assume that a proportion of these patients are cured and have no recurrence of the disease, known as the cure fraction. We further assume that the number of competing risks is random and follows a Poisson distribution. We consider the lifetimes of individuals to follow a two parameter generalized exponential distribution. The objective is to estimate the model parameters. Using a direct approach and the expectation maximization estimation approach, we obtain maximum likelihood estimates. Standard errors of the estimates are obtained by inverting the observed Fisher information matrix. Monte Carlo simulations are used to demonstrate the performance of the two methods of estimation. Finally, we fit our model to two real data sets to illustrate the model competence.