In this paper inverted Kumaraswamy distribution is introduced. Some of its properties are presented through, some models of stress strength, measures of central tendency and dispersion and order statistics. Some sub-models, limiting distributions and the relation between inverted Kumaraswamy and other distributions are derived. The maximum likelihood and Bayes estimators, confidence intervals for the parameters, the reliability and the hazard rate functions of the inverted Kumaraswamy distribution based on Type II censored samples are obtained. A numerical study is carried out to illustrate the theoretical results for both approaches, the maximum likelihood and the Bayesian estimation. Moreover, the results are applied on real data.