The complementary geometric transmuted-G family of distributions: Model, properties and application

We introduce a new family of continuous distributions called the complementary  geometric transmuted-$G$ family, which extends the transmuted family proposed by Shaw and Buckley (2007). Some of its  mathematical properties including explicit expressions for the ordinary and incomplete moments, quantile and generating functions, entropies, order statistics and probability weighted moments are derived. Two special models of the introduced family are discussed in detail. The  maximum likelihood method is used for estimating the model parameters. The importance and flexibility of the new family are illustrated by  means of two applications to real data sets. We provide some simulation results to assess the performance of the proposed model.