Abstarct: Kumaraswamy presented a probability density property for randomized two-side processes. For the first time, baxsed on this distribution, a new family of generalized distributions was created. Some special distributions, such as the Kumaraswamy Gamma, Kumaraswamy Normal, Kumaraswamy Weibull, ‎etc,‎ are discussed in the new family and we have obtained the moments and order statistics of these distributions. ‎we have used ‎The Maximum Likelihood Method for Estimating Generalized Distributions of Kumaraswamy and a simulation study for Type 1 censored data and Type II censored data, and for each censor, we estimate the parameters, the mean of second error, the ‎approximate‎ confidence interval, and the coverage rate. We also have examined parameters performance with pre-fixed values.‎