This paper discussed robust estimation methods for point estimation of the shape and scale parameters for Exponentiated Inverted Weibull Distribution) EIW) using a complete dataset in the presence of various percentages of outliers. In the case of outliers, it is known that classical methods such as maximum likelihood estimation (MLE), least square (LS) in case of outliers cannot reach the best estimator. To confirm this fact, these classical methods were applied to the data of this study and compared with non-classical estimation methods. The non-classical (Robust) methods such as least absolute deviations (LAD), and M-estimation (using M. Huber (MH) weight and M. Bi-square (MB) weight) had been introduced to obtain the best estimation method for the parameters of the EIW distribution. The comparison was done numerically by using the Monte Carlo simulation study. The real dataset application confirmed that the M-estimation method is very much suitable for estimating the EIW parameters. We concluded that the M-estimation method using Huber object function is a suitable estimation method in estimating the parameters of the EIW distribution for a complete dataset in the presence of various percentages of outliers