Multivariate Modified Dugum Distribution and Its Applications

Naelah Alghufily (), Khalaf S. Sultan and Hossam M. M. Radwan
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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

Mathematics, 2025, vol. 13, issue 10, 1-27

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.

Keywords: multivariate modified Dagum distribution; Clayton copula; multivariate dependence properties; maximum likelihood estimation; protein consumption and warranty policies data sets (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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