Abstract: The Kumaraswamy distribution is useful for modeling variables whose support is the standard unit interval, i.e., (0, 1). It is not uncommon, however, for the data to contain zeros and/or ones. When that happens, the interest shifts to modeling variables that assume values in [0, 1), (0, 1] or [0, 1]. Our goal in this paper is to introduce inflated Kumaraswamy distributions that can be used to that end. We consider inflation at one of the extremes of the standard unit interval and also the more challenging case in which inflation takes place at both interval endpoints. We introduce inflated Kumaraswamy distributions, discuss their main properties, show how to estimate their parameters (point and interval estimation) and explain how testing inferences can be performed. We also present Monte Carlo evidence on the finite sample performances of point estimation, confidence intervals and hypothesis tests. An empirical application is presented and discussed.