We introduce a new class of continuous distributions called the Kumaraswamy transmuted-G family which extends the transmuted class defined by
Shaw and Buckley (2007). Some special models of the new family are provided.
Some of its mathematical properties including explicit expressions for the
ordinary and incomplete moments, generating function, Rényi and Shannon
entropies, order statistics and probability weighted moments are derived. The
maximum likelihood is used for estimating the model parameters. The flexibility
of the generated family is illustrated by means of two applications to real data sets.