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The Stacy-G Class: A New Family of Distributions with Regression Modeling and Applications to Survival Real Data

Author

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  • Lucas D. Ribeiro Reis

    (Department of Statistics, Federal University of Pernambuco, Recife 50710-165, Brazil
    These authors contributed equally to this work.)

  • Gauss M. Cordeiro

    (Department of Statistics, Federal University of Pernambuco, Recife 50710-165, Brazil
    These authors contributed equally to this work.)

  • Maria do Carmo S. Lima

    (Department of Statistics, Federal University of Pernambuco, Recife 50710-165, Brazil
    These authors contributed equally to this work.)

Abstract

We study the Stacy-G family, which extends the gamma-G class and provides four of the most well-known forms of the hazard rate function: increasing, decreasing, bathtub, and inverted bathtub. We provide some of its structural properties. We estimate the parameters by maximum likelihood, and perform a simulation study to verify the asymptotic properties of the estimators for the Burr-XII baseline. We construct the log-Stacy-Burr XII regression for censored data. The usefulness of the new models is shown through applications to uncensored and censored real data.

Suggested Citation

  • Lucas D. Ribeiro Reis & Gauss M. Cordeiro & Maria do Carmo S. Lima, 2022. "The Stacy-G Class: A New Family of Distributions with Regression Modeling and Applications to Survival Real Data," Stats, MDPI, vol. 5(1), pages 1-43, March.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:1:p:15-257:d:764122
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    References listed on IDEAS

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    1. Paranaíba, Patrícia F. & Ortega, Edwin M.M. & Cordeiro, Gauss M. & Pescim, Rodrigo R., 2011. "The beta Burr XII distribution with application to lifetime data," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1118-1136, February.
    2. Ahmed Z. Afify & Gauss M. Cordeiro & Edwin M. M. Ortega & Haitham M. Yousof & Nadeem Shafique Butt, 2018. "The four-parameter Burr XII distribution: Properties, regression model, and applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(11), pages 2605-2624, June.
    3. Vasili B.V. Nagarjuna & R. Vishnu Vardhan & Christophe Chesneau, 2021. "Kumaraswamy Generalized Power Lomax Distributionand Its Applications," Stats, MDPI, vol. 4(1), pages 1-18, January.
    4. Ortega, Edwin M. M. & Bolfarine, Heleno & Paula, Gilberto A., 2003. "Influence diagnostics in generalized log-gamma regression models," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 165-186, February.
    5. Mustafa Ç. Korkmaz & Gauss M. Cordeiro & Haitham M. Yousof & Rodrigo R. Pescim & Ahmed Z. Afify & Saralees Nadarajah, 2019. "The Weibull Marshall–Olkin family: Regression model and application to censored data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(16), pages 4171-4194, August.
    6. Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 63-79, June.
    7. Gauss Moutinho Cordeiro & Maria Do Carmo Soares De Lima & Edwin Moisés Marcos Ortega & Adriano Kamimura Suzuki, 2018. "A New Extended Birnbaum–Saunders Model: Properties, Regression and Applications," Stats, MDPI, vol. 1(1), pages 1-16, May.
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