Modeling of air pollution and Lossalae data by using new classes of skew bivariate family distribution and extreme distributions

Osama Mohareb; Oluwafemi Samson Balogun; Zeinab Youssef; Mohamed Yusuf; Mahmoud E. Bakr; Mohammad Abiad; Yusra A. Tashkandy; Osama Mohareb; Oluwafemi Samson Balogun; Zeinab Youssef; Mohamed Yusuf; Mahmoud E. Bakr; Mohammad Abiad; Yusra A. Tashkandy

doi:10.3934/math.2025584

AIMS Mathematics

2025, Volume 10, Issue 6: 12980-13005. doi: 10.3934/math.2025584

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Research article

Modeling of air pollution and Lossalae data by using new classes of skew bivariate family distribution and extreme distributions

1.
Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said, Egypt
2.
Department of Computing, University of Eastern Finland, FI-70211, Finland
3.
Department of Mathematics, Faculty of Sciences, Damietta University, Damietta, Egypt
4.
Department of Mathematics, Faculty of Sciences, Helwan University, Egypt, mohammed
5.
Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
6.
College of Business Administration, American University of the Middle East, Kuwait

Received: 16 October 2024 Revised: 01 April 2025 Accepted: 03 April 2025 Published: 06 June 2025
MSC : 62E10, 62F10, 62H12, 62P12

Adding two more parameters for shaping provides a flexible way to make any basic bivariate distribution function (df) more adaptable. The extended bivariate dfs can better handle different kinds of bivariate data by including these parameters. They can handle a wide range of skewness and kurtosis indices well. The innovation lies in introducing a novel multiplicative bivariate stable-symmetric normal (MBSSN) distribution with two parameters, extending the conventional bivariate standard normal distribution. We conducted a detailed examination of the statistical properties of the MBSSN family and compared it to other significant competitors, such as generalized families of bivariate dfs, using real-world data like air pollution. The findings underscore the advantages and effectiveness of the MBSSN family in capturing the nuances of diverse datasets. We also applied the same methodology to develop a new two-parameter extension for two variations of bivariate extreme value distributions, which we then useed to analyze Lossalae datasets. This extension showcases the versatility and practicality of the proposed approach across different scenarios and distribution types.
- bivariate skew-normal distribution,
- mixtures of distributions,
- bivariate extremes,
- atmospheric contamination
Citation: Osama Mohareb, Oluwafemi Samson Balogun, Zeinab Youssef, Mohamed Yusuf, Mahmoud E. Bakr, Mohammad Abiad, Yusra A. Tashkandy. Modeling of air pollution and Lossalae data by using new classes of skew bivariate family distribution and extreme distributions[J]. AIMS Mathematics, 2025, 10(6): 12980-13005. doi: 10.3934/math.2025584

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Abstract

Adding two more parameters for shaping provides a flexible way to make any basic bivariate distribution function (df) more adaptable. The extended bivariate dfs can better handle different kinds of bivariate data by including these parameters. They can handle a wide range of skewness and kurtosis indices well. The innovation lies in introducing a novel multiplicative bivariate stable-symmetric normal (MBSSN) distribution with two parameters, extending the conventional bivariate standard normal distribution. We conducted a detailed examination of the statistical properties of the MBSSN family and compared it to other significant competitors, such as generalized families of bivariate dfs, using real-world data like air pollution. The findings underscore the advantages and effectiveness of the MBSSN family in capturing the nuances of diverse datasets. We also applied the same methodology to develop a new two-parameter extension for two variations of bivariate extreme value distributions, which we then useed to analyze Lossalae datasets. This extension showcases the versatility and practicality of the proposed approach across different scenarios and distribution types.

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