Advanced modeling of dependent structures using the FGM-quadratic exponential bivariate distribution: Applications in computer and material sciences

I. A. Husseiny; Abdulrahman M. A. Aldawsari; Asamh Saleh M. Al Luhayb; Reid Alotaibi; I. A. Husseiny; Abdulrahman M. A. Aldawsari; Asamh Saleh M. Al Luhayb; Reid Alotaibi

doi:10.3934/math.2025962

AIMS Mathematics

2025, Volume 10, Issue 9: 21642-21674. doi: 10.3934/math.2025962

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Advanced modeling of dependent structures using the FGM-quadratic exponential bivariate distribution: Applications in computer and material sciences

1.
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
2.
Department of Mathematics, College of Sciences and Humanities, Prince Sattam Bin Abdulaziz University, Al-Kharj 16273, Saudi Arabia
3.
Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
4.
Department of Mathematics, College of Science and Humanities, Shaqra University, Saudi Arabia

Received: 28 June 2025 Revised: 10 September 2025 Accepted: 12 September 2025 Published: 18 September 2025
MSC : 60B12, 62G30

Due to their ability to capture complex interactions between random variables, copula models are gaining increasing attention. When it comes to bivariate data modeling, one important area of statistical theory is the construction of families of distributions with specified marginals. An FGM-QEXD (bivariate quadratic exponential Farlie Gumbel Morgenstern distribution) is derived from the FGM copula and the new quadratic exponential marginal distribution, and is inspired by this. The statistical features of the FGM-QEXD are studied, encompassing: the conditional distribution, regression function, moment generating function, and correlation coefficient. Additionally, reliability measures were obtained, including the survival function, hazard rate function, mean residual life function, and vitality function. The model parameters are estimated via maximum likelihood (ML) and Bayesian methodologies. Furthermore, asymptotic confidence ranges for the model parameter are obtained. Monte Carlo simulation analysis is employed to evaluate the efficacy of both ML and Bayesian estimators. Two real-world datasets are employed to prove that FGM-QEXD is more flexible than the bivariate Weibull Farlie–Gumbel–Morgernstern (FGM), bivariate Lomax FGM, bivariate inverse Lomax FGM, bivariate Rayleigh FGM, bivariate Burr XII FGM, and bivariate Chen FGM distributions.
- Bayesian estimation,
- confidence intervals,
- FGM bivariate family,
- maximum likelihood estimation,
- simulation
Citation: I. A. Husseiny, Abdulrahman M. A. Aldawsari, Asamh Saleh M. Al Luhayb, Reid Alotaibi. Advanced modeling of dependent structures using the FGM-quadratic exponential bivariate distribution: Applications in computer and material sciences[J]. AIMS Mathematics, 2025, 10(9): 21642-21674. doi: 10.3934/math.2025962

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Abstract

Due to their ability to capture complex interactions between random variables, copula models are gaining increasing attention. When it comes to bivariate data modeling, one important area of statistical theory is the construction of families of distributions with specified marginals. An FGM-QEXD (bivariate quadratic exponential Farlie Gumbel Morgenstern distribution) is derived from the FGM copula and the new quadratic exponential marginal distribution, and is inspired by this. The statistical features of the FGM-QEXD are studied, encompassing: the conditional distribution, regression function, moment generating function, and correlation coefficient. Additionally, reliability measures were obtained, including the survival function, hazard rate function, mean residual life function, and vitality function. The model parameters are estimated via maximum likelihood (ML) and Bayesian methodologies. Furthermore, asymptotic confidence ranges for the model parameter are obtained. Monte Carlo simulation analysis is employed to evaluate the efficacy of both ML and Bayesian estimators. Two real-world datasets are employed to prove that FGM-QEXD is more flexible than the bivariate Weibull Farlie–Gumbel–Morgernstern (FGM), bivariate Lomax FGM, bivariate inverse Lomax FGM, bivariate Rayleigh FGM, bivariate Burr XII FGM, and bivariate Chen FGM distributions.

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