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Bivariate Unit-Weibull Distribution: Properties and Inference

Author

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  • Roger Tovar-Falón

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Monteria 230002, Colombia
    These authors contributed equally to this work.)

  • Guillermo Martínez-Flórez

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Monteria 230002, Colombia
    These authors contributed equally to this work.)

  • Luis Páez-Martínez

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Monteria 230002, Colombia)

Abstract

In this article, we introduce a novel bivariate probability distribution that is absolutely continuous. Considering the Farlie–Gumbel–Morgenstern (FGM) copula and the unit-Weibull distribution, we can obtain a bivariate unit-Weibull distribution. We evaluate the main properties of the new proposal and use two estimation methods to estimate the parameter for the bivariate probability distribution. A brief Monte Carlo simulation study is conducted to assess the behavior of the employed estimation method and the characteristics of the estimators. Ultimately, as an illustration, a real-life application is presented, demonstrating the utility of the proposal.

Suggested Citation

  • Roger Tovar-Falón & Guillermo Martínez-Flórez & Luis Páez-Martínez, 2023. "Bivariate Unit-Weibull Distribution: Properties and Inference," Mathematics, MDPI, vol. 11(17), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3760-:d:1230757
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    References listed on IDEAS

    as
    1. Guillermo Martínez-Flórez & Rafael Bráz Azevedo-Farias & Roger Tovar-Falón, 2022. "An Exponentiated Multivariate Extension for the Birnbaum-Saunders Log-Linear Model," Mathematics, MDPI, vol. 10(8), pages 1-17, April.
    2. Ehab Mohamed Almetwally & Hiba Zeyada Muhammed & El-Sayed A. El-Sherpieny, 2020. "Bivariate Weibull Distribution: Properties and Different Methods of Estimation," Annals of Data Science, Springer, vol. 7(1), pages 163-193, March.
    3. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    4. Guillermo Martínez-Flórez & Sandra Vergara-Cardozo & Roger Tovar-Falón & Luisa Rodriguez-Quevedo, 2023. "The Multivariate Skewed Log-Birnbaum–Saunders Distribution and Its Associated Regression Model," Mathematics, MDPI, vol. 11(5), pages 1-21, February.
    5. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
    6. Paolino, Philip, 2001. "Maximum Likelihood Estimation of Models with Beta-Distributed Dependent Variables," Political Analysis, Cambridge University Press, vol. 9(4), pages 325-346, January.
    7. Donald G. Freeman, 2007. "Drunk Driving Legislation And Traffic Fatalities: New Evidence On Bac 08 Laws," Contemporary Economic Policy, Western Economic Association International, vol. 25(3), pages 293-308, July.
    Full references (including those not matched with items on IDEAS)

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