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For any continuous baseline G distribution, Zografos and Balakrishnan On families of beta- and generalized gamma-generated distributions and associated inference. Statist Methodol. 2009;6:344–362 proposed a generalized gamma-generated distribution with an extra positive parameter. A new three-parameter continuous distribution called the gamma-Lomax distribution, which extends the Lomax distribution is proposed and studied. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile functions, mean deviations and Rényi entropy. The estimation of the model parameters is performed by maximum likelihood. We also determine the observed information matrix. An application illustrates the usefulness of the proposed model.
Cordeiro et al. (Thu,) studied this question.