Important distributions used to model and analyse data in various real-life sciences such as natural sciences, engineering, and medicine are the Weibull distribution, the Weibull exponential distribution, and the Weibull Rayleigh distribution. The main objective of this paper is to determine the best evaluators and compare them for the distribution with three-parameters of Weibull, Weibull Rayleigh and Exponential Weibull. The methods under consideration for comparing the parameter estimators for these distributions is that of maximum likelihood using the statistical program R for the application of real data. Based on the results obtained from this study, the maximum likelihood approach used in estimating the parameters is the comparison between these distributions. Comparisons are made to determine the performance of these distributions.