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The Gamma Power Generalized Weibull Distribution: Modeling Bibliometric Data

Author

Listed:
  • Arioane Primon Soares

    (Federal Institute of Education, Science and Technology Farroupilha (IFFar), Alameda Santiago do Chile 195, Santa Maria 97050-685, Brazil)

  • Ryan Novaes Pereira

    (Department of Statistics, Faculty of Science and Technology, São Paulo State University (UNESP), Rua Sen. Roberto Simonsen 305, Presidente Prudente 19060-080, Brazil)

  • Fernando A. Peña-Ramírez

    (Department of Statistics, Center for Exact and Natural Sciences, Federal University of Santa Maria, Av. Roraima 1000, Santa Maria 97105-340, Brazil)

  • Luz Milena Zea Fernández

    (Department of Statistics, Center for Exact and Earth Sciences, Federal University of Rio Grande do Norte, Av. Senador Salgado Filho 3000, Natal 59078-900, Brazil)

  • Renata Rojas Guerra

    (Department of Statistics, Center for Exact and Natural Sciences, Federal University of Santa Maria, Av. Roraima 1000, Santa Maria 97105-340, Brazil)

Abstract

In this study, we introduce the gamma power generalized Weibull (GPGW) distribution and investigate several of its main mathematical properties. The performance of the maximum likelihood estimators is evaluated through Monte Carlo simulations. The practical relevance of the proposed distribution is illustrated through an application to real bibliometric data, where the GPGW is used to model SCImago Journal Rank (SJR) indicators. In comparison with alternative models commonly employed for lifetime and positive data, the GPGW distribution exhibits strong competitive performance. In particular, in the real data application, it outperforms eleven competing distributions in terms of goodness of fit criteria, including the power generalized Weibull (PGW), the gamma-Nadarajah–Haghighi (GNH), and the exponentiated power generalized Weibull (EPGW) distributions. While inheriting several mathematical features of the EPGW distribution, such as expressions for moments, skewness, and kurtosis, the GPGW offers enhanced flexibility, making it a valuable modeling tool for lifetime data and heavy-tailed positive measurements.

Suggested Citation

  • Arioane Primon Soares & Ryan Novaes Pereira & Fernando A. Peña-Ramírez & Luz Milena Zea Fernández & Renata Rojas Guerra, 2026. "The Gamma Power Generalized Weibull Distribution: Modeling Bibliometric Data," Stats, MDPI, vol. 9(2), pages 1-17, March.
    • Handle: RePEc:gam:jstats:v:9:y:2026:i:2:p:26-:d:1878360
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