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.

In order to choose the right statistical test, when analyzing the data from an experiment, we must have at least a decent understanding of some basic statistical terms and concepts; some knowledge about few aspects related to the data we collected during the research/experiment (e.g. what types of data we have - samples, normal distribution with parameters, power of tests, how the data are organized, how many study groups (usually experimental and control at least) we have, are the samples paired or unpaired, and are the sample(s) extracted from a normally distributed/Gaussian population);a good understanding of the goal of our statistical analysis; we have to parse the entire statistical protocol in an well structured - decision tree /algorithmic manner, in order to avoid some mistakes.