The modeling and analysis of lifetimes is an important aspect of statistical work in a wide variety of scientific and technological fields. In recent years it is observed that inverted Kumaraswamy distribution has been used quite effectively to model many lifetime data. The main objective of this research is to construct a generalized inverted Kumaraswamy distribution based on M mixture representation. Also, this research is to develop a general form of inverted Kumaraswamy distribution which is flexible more than the inverted Kumaraswamy distribution and all of its related and submodules. Some properties of the generalized inverted Kumaraswamy distribution such as probability density function and cumulative distribution function are presented. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is derived. Also, the Bayesian method is used to obtain the estimators of the parameters. A simulation study is carried out to illustrate the theoretical results of the maximum likelihood estimation and Bayesian estimation. Finally, the importance and flexibility of the new model of real data set are proved empirically.