The q-Weibull distribution is a flexible probability distribution that is commonly used in reliability analysis, survival analysis, and extreme value modelling. Obtaining accurate parameter estimates is essential for these applications. This paper investigates several estimation techniques for the q-Weibull distribution, with special emphasis on the Metropolis–Hastings algorithm. Through an extensive simulation study, we evaluate the performance of these methods across different sample sizes. In addition, we apply them to a real dataset to illustrate their practical utility and to highlight situations where the Metropolis–Hastings approach proves particularly advantageous.