Least-squares and minimum chi-square estimation in a discrete Weibull model

In this work, we investigate the properties of least-squares and minimum chi-square methods for the point estimation of the two parameters characterizing a discrete Weibull distribution. The first method, inflected into three variants, is based on the empirical cumulative distribution function and provides a closed analytical expression for each estimate. The second method is based on the minimization of the well-known chi-square statistic, which provides a numerical solution. A Monte Carlo simulation study empirically assesses the performance of the methods; two applications on real data show how the inferential techniques practically work.