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).

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In this paper, the parameters of the Modified Weibull Extension Distribution are estimated using the maximum likelihood estimator method and the Monte Carlo method in the simulation procedure to generate many different sample sizes, with many different replicates of the sample sizes. Following that finding, the Survival function’s estimate. Then fuzzify the estimation of the parameters for the same different sample sizes with the same difference in replicated sample sizes that was obtained from the Monte Carlo method in the simulation procedure by the new proposed method of expanding the Confidence Interval of estimated parameters to nine fuzzy numbers. Then, transform all the fuzzy parameters to crisp parameters using the proposed ranking functions with (proposed Linear Two- Symmetric Pentagonal Fuzzy Numbers, and proposed Non Linear Two-Symmetric Pentagonal Fuzzy Numbers). Accordingly, finding the Survival function. The outcome of Survival functions before and after fuzzy work will be compared using mean square error.