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Marshall–Olkin Bivariate Weibull Model with Modified Singularity (MOBW- μ ): A Study of Its Properties and Correlation Structure

Author

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  • Hugo Brango

    (Departamento de Matemáticas y Estadística, Universidad del Norte, Barranquilla 080001, Colombia
    These authors contributed equally to this work.)

  • Angie Guerrero

    (Departamento de Matemáticas y Estadística, Universidad del Norte, Barranquilla 080001, Colombia
    These authors contributed equally to this work.)

  • Humberto Llinás

    (Departamento de Matemáticas y Estadística, Universidad del Norte, Barranquilla 080001, Colombia
    These authors contributed equally to this work.)

Abstract

We propose the “Marshall–Olkin Bivariate Weibull Model with Modified Singularity MOBW- μ ”, which focuses on bivariate distributions essential for reliability and survival analyses. Distributions such as the Marshall–Olkin bivariate exponential (MOBE) and the Marshall–Olkin bivariate Weibull (MOBW) are discussed. The MOBW- μ model is introduced, which incorporates a lag parameter μ in the singular part, and probabilistic properties such as the joint survival function, marginal density functions, and the bivariate hazard rate function are explored. In addition, aspects such as the correlation structure and survival copulation are addressed and we show that the correlation of the MOBW- μ is always lower than that of its copula, regardless of the parameters. The latter result implies that the MOBW- μ does not have the Lancaster’s phenomenon that explains that any nonlinear transformation of variables decreases the correlation in absolute value. The article concludes by presenting a robust theoretical framework applicable to various disciplines.

Suggested Citation

  • Hugo Brango & Angie Guerrero & Humberto Llinás, 2024. "Marshall–Olkin Bivariate Weibull Model with Modified Singularity (MOBW- μ ): A Study of Its Properties and Correlation Structure," Mathematics, MDPI, vol. 12(14), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2183-:d:1433557
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    References listed on IDEAS

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    2. Li, Xiaohu & Pellerey, Franco, 2011. "Generalized Marshall-Olkin distributions and related bivariate aging properties," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1399-1409, November.
    3. Papadatos, Nickos & Xifara, Tatiana, 2013. "A simple method for obtaining the maximal correlation coefficient and related characterizations," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 102-114.
    4. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
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