In this work, we consider the Weibull distribution of two parameters for its importance in statistics and its applications. Mathematical and statistical properties of Weibull distribution are considered, moments and higher moments are illustrated and unified. Four methods of estimation to the distribution parameters namely (Maximum likelihood Method, Moments Method, Modified Moments Method, Least Square Method) are discussed theoretically and assessed practically by utilizing six procedures of Monte-Carlo simulation for generating random variates from the distribution. Efficiency of some procedures are found theoretically and compared practically. Comparisons are made among four methods of estimation by considering the mean square error measurement.