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Multivariate Modified Dugum Distribution and Its Applications

Author

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  • Naelah Alghufily

    (Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Khalaf S. Sultan

    (Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo 11884, Egypt)

  • Hossam M. M. Radwan

    (Mathematics Department, Faculty of Science, Minia University, Minia 61519, Egypt)

Abstract

The modified Dagum distribution is a highly versatile statistical model, and it is included in several important parametric families of distributions, with applications, such as economics and public health. In this paper, we introduce a multivariate version of the modified Dagum distribution and deduce some of its sub-models to address specific analytical needs. We use two different approaches to derive the joint probability density function for the proposed distribution. Also, we derive the joint cumulative distribution function through the traditional method and the Clayton copula methods. In addition, we explore and discuss some statistical properties, including the multivariate dependence. Further, we use the maximum likelihood method to estimate the unknown parameters and the associated confidence interval. Finally, we apply the proposed model to analyze some real data sets, including a protein consumption data set and a warranty policy data set, for demonstrative purposes. The marginals of the proposed model fit the data sets quite well, and the results demonstrate the model’s effectiveness in modeling the proposed data.

Suggested Citation

  • Naelah Alghufily & Khalaf S. Sultan & Hossam M. M. Radwan, 2025. "Multivariate Modified Dugum Distribution and Its Applications," Mathematics, MDPI, vol. 13(10), pages 1-27, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1620-:d:1656334
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    References listed on IDEAS

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    1. Christian Kleiber, 2008. "A Guide to the Dagum Distributions," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 6, pages 97-117, Springer.
    2. Felipe Gusmão & Edwin Ortega & Gauss Cordeiro, 2011. "The generalized inverse Weibull distribution," Statistical Papers, Springer, vol. 52(3), pages 591-619, August.
    3. Peng, Xiuyun & Yan, Zaizai, 2014. "Estimation and application for a new extended Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 34-42.
    4. Domma, Filippo & Condino, Francesca & Giordano, Sabrina, 2018. "A new formulation of the Dagum distribution in terms of income inequality and poverty measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 104-126.
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