A New Bivariate Family of Distributions Based on the Clayton Archimedean Copula and Dagum Distribution

https://doi.org/10.51867/ajernet.6.1.50

Authors

Keywords:

Bivariate, Clayton Copula, Dagum Distribution, Statistical Properties, Joint Moments, Entropy

Abstract

This study introduces a novel bivariate distribution combining the Clayton Archimedean copula and the Dagum distribution, addressing challenges in modeling complex dependencies, skewness, heavy tails, and multimodal distributions. The proposed NBCDagE distribution leverages the Clayton copula’s ability to capture asymmetric dependencies and the Dagum distribution’s flexibility to model diverse data behaviors, making it suitable for reliability, finance, and survival analysis applications. Key statistical properties of the NBCDagE distribution, including the probability density function (PDF), cumulative distribution function (CDF), product and joint moments, and Shannon entropy, were derived and analyzed. The model demonstrates sensitivity to parameter changes, with higher parameter values leading to sharper PDFs and lighter tails, while lower values result in flatter PDFs and heavier tails. Joint moments and entropy analyses revealed the distribution’s ability to adapt to varying data complexities, showcasing its robustness in capturing dependence structures and marginal characteristics. Visual representations, including contour plots and density curves, illustrate the flexibility of the NBCDagE model in handling a wide range of dependence patterns and data structures. The distribution’s performance was further validated through theoretical derivations and numerical examples, highlighting its adaptability and precision in multivariate data modeling. In conclusion, the NBCDagE distribution provides a robust framework for analyzing bivariate data with intricate dependency structures. Its flexibility and statistical rigor make it a valuable tool for diverse applications, paving the way for future research in higher-dimensional extensions and practical implementations.

Dimensions

Al-Shomrani, A. A. (2023). New bivariate family of distributions based on any copula function: Statistical properties. Heliyon, 9(4). https://doi.org/10.1016/j.heliyon.2023.e15160 DOI: https://doi.org/10.1016/j.heliyon.2023.e15160

Aldhufairi, F. A. A., & Sepanski, J. H. (2024). New Bivariate Copulas via Lomax Distribution Generated Distortions. AppliedMath, 4(2), 641-665.

https://doi.org/10.3390/appliedmath4020035 DOI: https://doi.org/10.3390/appliedmath4020035

Alotaibi, R., Rezk, H., Dey, S., & Okasha, H. (2021). Bayesian estimation for Dagum distribution based on progressive type I interval censoring. PLOS ONE, 16(6), e0252556.

https://doi.org/10.1371/journal.pone.0252556 DOI: https://doi.org/10.1371/journal.pone.0252556

Bechiri, S., & Remita, M. R. (2024). On Dagum-Pareto mixture distribution: properties, simulation, and application in insurance. Studies in Engineering and Exact Sciences, 5(2), e7530-e7530.

https://doi.org/10.54021/seesv5n2-165 DOI: https://doi.org/10.54021/seesv5n2-165

Chama, A. F., Abdulkadir, S. S., & Akinrefon, A. A. (2024). Cure Rate Model in Survival Analysis Using Cubic Transmuted Dagum Distribution. European Journal of Applied Science, Engineering and Technology, 2(4), 117-125. https://doi.org/10.59324/ejaset.2024.2(4).08 DOI: https://doi.org/10.59324/ejaset.2024.2(4).08

Coia, V. (2017). Forecasting of nonlinear extreme quantiles using copula models (Doctoral dissertation, University of British Columbia).

Cooray, K. (2019). A new extension of the FGM copula for negative association. Communications in Statistics- Theory and Methods, 48(8), 1902-1919.

https://doi.org/10.1080/03610926.2018.1440312 DOI: https://doi.org/10.1080/03610926.2018.1440312

Dagum, C. (1977). A New Model for Personal Income Distribution: Specification and Estimation. Economie Appliqu'ee, 30, 413-437.

https://doi.org/10.3406/ecoap.1977.4213 DOI: https://doi.org/10.3406/ecoap.1977.4213

de Sousa Neves, G. (2022). Models for Forecasting Value at Risk: A Comparison of the Predictive Ability of Different VaR Models to Capture Market Losses Incurred During the 2020 Pandemic Recession (Master's thesis, Universidade NOVA de Lisboa (Portugal)).

Dey, S., Al-Zahrani, B., & Basloom, S. (2017). Dagum distribution: Properties and different methods of estimation. International Journal of Statistics and Probability, 6(2), 74-92.

https://doi.org/10.5539/ijsp.v6n2p74 DOI: https://doi.org/10.5539/ijsp.v6n2p74

El-Sherpieny, E. S. A., Muhammed, H. Z., & Almetwally, E. M. (2022). Bivariate Chen distribution based on copula function: Properties and application of diabetic nephropathy. Journal of Statistical Theory and Practice, 16(3), 54.

https://doi.org/10.1007/s42519-022-00275-7 DOI: https://doi.org/10.1007/s42519-022-00275-7

El-Sherpieny, E. S., & Almetwally, E. M. (2019, December). Bivariate generalized rayleigh distribution based on Clayton Copula. In Proceedings of the annual conference on statistics (54rd), computer science and operation research, faculty of graduate studies for statistical research, Cairo University (pp. 1-19).

Fang, G., & Pan, R. (2021). On multivariate copula modeling of dependent degradation processes. Computers & Industrial Engineering, 159, 107450.

https://doi.org/10.1016/j.cie.2021.107450 DOI: https://doi.org/10.1016/j.cie.2021.107450

Febriantikasari, E., Adnan, A., Yendra, R., & Muhaijir, M. N. (2019). Using Dagum Distribution to Simulated Concentration PM10 in Pekanbaru City, Indonesia. Applied Mathematical Sciences, 13(9), 439- 448. https://doi.org/10.12988/ams.2019.9347 DOI: https://doi.org/10.12988/ams.2019.9347

Ghalibaf, M. B. (2022). Stress-strength reliability with dependent variables based on copula function. Journal of Dynamics & Games, 9(3). https://doi.org/10.3934/jdg.2022014 DOI: https://doi.org/10.3934/jdg.2022014

Hao, Z., & Singh, V. P. (2016). Review of dependence modeling in hydrology and water resources. Progress in Physical Geography, 40(4), 549-578.

https://doi.org/10.1177/0309133316632460 DOI: https://doi.org/10.1177/0309133316632460

Ishaq, A. I., & Abiodun, A. A. (2020). A new generalization of Dagum distribution with application to financial data sets. In 2020 International Conference on Data Analytics for Business and Industry: Way Towards a Sustainable Economy (ICDABI) (pp. 1-6). IEEE. https://doi.org/10.1109/ICDABI51230.2020.9325637 DOI: https://doi.org/10.1109/ICDABI51230.2020.9325637

Kularatne, T. D., Li, J., & Pitt, D. (2021). On the use of Archimedean copulas for insurance modelling.

https://doi.org/10.1017/S1748499520000147 DOI: https://doi.org/10.1017/S1748499520000147

Annals of Actuarial Science, 15(1), 57-81.

Li, F., & Kang, Y. (2018). Improving forecasting performance using covariate-dependent copula models.

https://doi.org/10.1016/j.ijforecast.2018.01.007 DOI: https://doi.org/10.1016/j.ijforecast.2018.01.007

International Journal of Forecasting, 34(3), 456-476.

Nassir, L. M., & Ibrahim, N. A. (2020). The Bayesian estimator for probabilistic dagum distribution.

International Journal of Innovation, Creativity and Change, 12(5), 42-74.

Nelsen, R. B. (2006). An introduction to copulas.

Oh, D. H., & Patton, A. J. (2017). Modeling dependence in high dimensions with factor copulas. Journal of Business & Economic Statistics, 35(1), 139-154.

https://doi.org/10.1080/07350015.2015.1062384 DOI: https://doi.org/10.1080/07350015.2015.1062384

Okorie, I. E., Akpanta, A. C., & Osu, B. O. (2019). Flexible heavy tail distributions for Surface ozone for selected sites in the United States of America. Ozone: Science & Engineering, 41(5), 473-488. https://doi.org/10.1080/01919512.2019.1566693 DOI: https://doi.org/10.1080/01919512.2019.1566693

Oluyede, B. O., & Ye, Y. (2014). Weighted Dagum and related distributions. Afrika Matematika, 25, 1125- 1141.

https://doi.org/10.1007/s13370-013-0176-0 DOI: https://doi.org/10.1007/s13370-013-0176-0

Oneto, L. (2020). Model selection and error estimation in a nutshell. Springer International Publishing.

https://doi.org/10.1007/978-3-030-24359-3 DOI: https://doi.org/10.1007/978-3-030-24359-3

Peres, M. V. D. O., Achcar, J. A., & Martinez, E. Z. (2018). Bivariate modified Weibull distribution derived from Farlie-Gumbel-Morgenstern copula: a simulation study. Electronic Journal of Applied Statistical Analysis, 11(2), 463-488.

Prasad, A. S. (2020). Dependence: From classical copula modeling to neural networks.

Samanthi, R. G. M., & Sepanski, J. (2022). On bivariate Kumaraswamy-distorted copulas. Communications in Statistics-Theory and Methods, 51(8), 2477-2495.

https://doi.org/10.1080/03610926.2020.1777303 DOI: https://doi.org/10.1080/03610926.2020.1777303

Saraiva, E. F., Suzuki, A. K., & Milan, L. A. (2018). Bayesian computational methods for sampling from the posterior distribution of a bivariate survival model, based on AMH copula in the presence of right-censored data. Entropy, 20(9), 642.

https://doi.org/10.3390/e20090642 DOI: https://doi.org/10.3390/e20090642

Shankar, P. M., & Shankar, P. M. (2021). Multiple Random Variables and Their Characteristics. Probability, Random Variables, and Data Analytics with Engineering Applications, 233-336. https://doi.org/10.1007/978-3-030-56259-5_4 DOI: https://doi.org/10.1007/978-3-030-56259-5_4

Sosa-Cabrera, G., Garc'ıa-Torres, M., G'omez-Guerrero, S., Schaerer, C. E., & Divina, F. (2019). A multivariate approach to the symmetrical uncertainty measure: Application to feature selection problem. Information Sciences, 494, 1-20.

https://doi.org/10.1016/j.ins.2019.04.046 DOI: https://doi.org/10.1016/j.ins.2019.04.046

Sun, F., Zhang, W., Wang, N., & Zhang, W. (2019). A copula entropy approach to dependence measurement for multiple degradation processes. Entropy, 21(8), 724.

https://doi.org/10.3390/e21080724 DOI: https://doi.org/10.3390/e21080724

Tahir, M. H., Hussain, M. A., Cordeiro, G. M., El-Morshedy, M., & Eliwa, M. S. (2020). A new Kumaraswamy generalized family of distributions with properties, applications, and bivariate extension. Mathematics, 8(11), 1989.

https://doi.org/10.3390/math8111989 DOI: https://doi.org/10.3390/math8111989

Zhang, Y., Kim, C. W., Beer, M., Dai, H., & Soares, C. G. (2018). Modeling multivariate ocean data using asymmetric copulas. Coastal Engineering, 135, 91-111.

https://doi.org/10.1016/j.coastaleng.2018.01.008 DOI: https://doi.org/10.1016/j.coastaleng.2018.01.008

Published

2025-03-04

How to Cite

Adu-Ntim, J. K., Omari-Sasu, A. Y., Boateng, M. A., & Mensah, I. A. (2025). A New Bivariate Family of Distributions Based on the Clayton Archimedean Copula and Dagum Distribution. African Journal of Empirical Research, 6(1), 580–603. https://doi.org/10.51867/ajernet.6.1.50

Issue

Vol. 6 No. 1 (2025): Jan-Mar 2025

Section

Articles
Copyright & Licensing

Copyright (c) 2025 Julius Kwaku Adu-Ntim, Akoto Yaw Omari-Sasu, Maxwell Akwasi Boateng, Isaac Adjei Mensah

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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