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In this article the Exponentiated Weibull distribution with some of its properties is considered. Classical methods, Maximum likelihood estimator method, ordinary least squares estimator method and rank set sampling estimator method are proposed to estimate all the unknown parameters (β,Ψ,θ) of the distribution. Newton–Raphson method is used to solve the above three methods, simulation procedure is used to generated some sample sizes and finally mean squares error measure are used to compare between them. We find Maximum likelihood estimator method has the smallest mean square error.

In this paper we introduced some of properties of the Exponentiated Weibull distribution. Tierney estimator method and Lindely estimator method are proposed to estimate all the unknown parameters (β,Ψ,θ) of the Exponentiated Weibull distribution. Simulation procedure is used to generate some sample sizes and mean squares error measure, and when we compared between the above two methods we find that Tierney method has the less (MSE).