Hill estimator, based on the order statistics, is one of the most widely used tools for determining the thickness parameter (tail index) of 2-parameter Pareto distribution heavy tails. Distribution tails are of paramount importance for engineering design and reliability assessments. In practical applications, however, the Hill estimator has to be modified to incorporate at least shift and scale parameters, as the original estimator is not shift and scale invariant. In practical engineering applications, however, distribution tails are not fat (heavy, thick), but instead thin, e.g., Weibull type. Fortunately, the Hill-type estimator can be modified to serve Weibull-type distributions. This study addresses novel 4-parameter Weibull distribution, which extends classic 2-parameter Weibull distribution. The primary challenge is that computational efforts, prediction inaccuracies and numerical instabilities increase with an increase of number of distribution parameters. Previously Levenberg-Marquardt Least-Squares (LMLS) optimization scheme was adopted to assess four parameters of the 4-parameter Weibull-type distribution. However, LMLS optimization proved to be often numerically unstable, lacking convergence criteria. This study presents a novel Maximum Likelihood Estimator (conditional MLE) based estimator, as a step forward in both parameter convergence and most importantly, answering the main designer question: does the selected distribution model fit underlying data at all. Renewable energy application (offshore wind speeds dynamics) was chosen to benchmark and validate proposed methodology. Novelty: presented study for the first time formulates semi-analytical solution for the 4-parameter Weibull distribution.