The paper proposes the "exponentiated generalized" (EG) class of distributions, a new method of adding two shape parameters to existing continuous distributions using a double Lehmann alternative construction. This extends the flexibility of distributions, particularly in the tails, enabling improved modeling in various fields. The study explores mathematical properties, including moments, generating functions, and order statistics, and demonstrates applications to real datasets from diverse areas like agriculture and material science, finding superior fits compared to existing models.

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The paper introduces a novel and flexible distribution family with sound mathematical foundations. The extensions using Lehmann alternatives and the derivations of various properties are valuable contributions. However, the limitations in model comparison, lack of exploration of practical implications of the infinite series expansions, and unclear motivation for specific EG variations hold it back from a top rating.