The type I discrete Weibull distribution can be used in reliability problems for modeling discrete failure data, such as the number of shocks, cycles, or runs a component or structure can overcome before failing. This paper refines and compares some existing methods for estimating its parameters and proposes and evaluates approximate confidence intervals for large samples. A Monte Carlo simulation study was performed in order to assess the statistical performance of the methods for different

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... ameter combinations and sample sizes and then give some indication for their mindful use. Examples are considered as a practical application of the proposed procedures. A software implementation of the model is provided as a contributed package in the R programming environment, which reveals a useful and friendly tool for the researcher who has to handle discrete Weibull data.