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This paper considers some computational issues related to the problem of the coupon collector behavior. In addition, we propose a simulation algorithm to find the solution to the problem, where we present as a numerical illustration an album of stickers related to the Qatar 2022 Official Football World Cup, which is being sold in Brazilian newsstands. In this case, the complete album has N = 670 stickers, which are sold in packages containing n = 5 stickers each. The simulation was based on a computational code written in R. For this application we obtained as a solution, an average number of 950 packages needed to complete the album, at an average cost of 3,800 reals (Brazilian currency), assuming that the collector does not exchange any of its repetitions with nobody. All computer code used in this article is provided on GitHub. The assumed simulation study could be useful for statistics teachers to motivate their students for lectures in computational statistics and fundamentals of probability., Comment: 9 pages, 5 figures

This paper presents inferences for the discrete Bilal (DB) distribution introduced by Altun et al. (2020). We consider parameter estimation for DB distribution in the presence of randomly right-censored data.We use maximum likelihood and Bayesian methods for the estimation of the model parameters. We also consider the inclusion of a cure fraction in the model. The usefulness of the proposed model was illustrated with three examples considering real datasets. These applications suggested that the model based on DB distribution performs at least as good as some other traditional discrete models as the DsFx-I, discrete Lindley, discrete Rayleigh, and discrete Burr- Hatke distributions. R codes are provided in an appendix at the end of the paper so that reader can carry out their own analysis., Comment: 20 pages, 10 figures

In medical studies, it is common the presence of a fraction of patients who do not experience the event of interest. These patients are people who are not at risk of the event or are patients who were cured during the research. The proportion of immune or cured patients is known in the literature as cure rate. In general, the traditional existing lifetime statistical models are not appropriate to model data sets with cure rate, including bivariate lifetimes. In this paper, it is proposed a bivariate model based on a defective Gompertz distribution and also using a Clayton copula function to capture the possible dependence structure between the lifetimes. An extensive simulation study was carried out in order to evaluate the biases and the mean squared errors for the maximum likelihood estimators of the parameters associated to the proposed distribution. Some applications using medical data are presented to show the usefulness of the proposed model.

In this paper, we discuss computational aspects to obtain accurate inferences for the parameters of the generalized gamma (GG) distribution. Usually, the solution of the maximum likelihood estimators (MLE) for the GG distribution have no stable behavior depending on large sample sizes and good initial values to be used in the iterative numerical algorithms. From a Bayesian approach, this problem remains, but now related to the choice of prior distributions for the parameters of this model. We presented some exploratory techniques to obtain good initial values to be used in the iterative procedures and also to elicited appropriate informative priors. Finally, our proposed methodology is also considered for data sets in the presence of censorship.