A novel bivariate Lomax-G family of distributions: Properties, inference, and applications to environmental, medical, and computer science data

Aisha Fayomi; Ehab M. Almetwally; Maha E. Qura; Aisha Fayomi; Ehab M. Almetwally; Maha E. Qura

doi:10.3934/math.2023896

AIMS Mathematics

2023, Volume 8, Issue 8: 17539-17584. doi: 10.3934/math.2023896

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A novel bivariate Lomax-G family of distributions: Properties, inference, and applications to environmental, medical, and computer science data

1.
Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia, Email: afayomi@kau.edu.sa
2.
Department of Statistical, Faculty of Business Administration, Delta University for Science and Technology, Gamasa 11152, Egypt, Email: ehab.metwaly@deltauniv.edu.eg
3.
Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt, Email: maha.qura@fcom.bu.edu.eg

Received: 21 March 2023 Revised: 25 April 2023 Accepted: 08 May 2023 Published: 22 May 2023
MSC : 62H10, 34A12, 62F15

This paper presents a novel family of bivariate continuous Lomax generators known as the BFGMLG family, which is constructed using univariate Lomax generator (LG) families and the Farlie Gumbel Morgenstern (FGM) copula. We have derived several structural statistical properties of our proposed bivariate family, such as marginals, conditional distribution, conditional expectation, product moments, moment generating function, correlation, reliability function, and hazard rate function. The paper also introduces four special submodels of the new family based on the Weibull, exponential, Pareto, and log-logistic baseline distributions. The study establishes metrics for local dependency and examines the significant characteristics of the proposed bivariate model. To provide greater flexibility, a multivariate version of the continuous FGMLG family are suggested. Bayesian and maximum likelihood methods are employed to estimate the model parameters, and a Monte Carlo simulation evaluates the performance of the proposed bivariate family. Finally, the practical application of the proposed bivariate family is demonstrated through the analysis of four data sets.
- bivariate Lomax-G family of distributions,
- Lomax-G family of distributions,
- multivariate distributions,
- dependence concepts,
- skewed distribution,
- Bayesian estimation
Citation: Aisha Fayomi, Ehab M. Almetwally, Maha E. Qura. A novel bivariate Lomax-G family of distributions: Properties, inference, and applications to environmental, medical, and computer science data[J]. AIMS Mathematics, 2023, 8(8): 17539-17584. doi: 10.3934/math.2023896

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Abstract

This paper presents a novel family of bivariate continuous Lomax generators known as the BFGMLG family, which is constructed using univariate Lomax generator (LG) families and the Farlie Gumbel Morgenstern (FGM) copula. We have derived several structural statistical properties of our proposed bivariate family, such as marginals, conditional distribution, conditional expectation, product moments, moment generating function, correlation, reliability function, and hazard rate function. The paper also introduces four special submodels of the new family based on the Weibull, exponential, Pareto, and log-logistic baseline distributions. The study establishes metrics for local dependency and examines the significant characteristics of the proposed bivariate model. To provide greater flexibility, a multivariate version of the continuous FGMLG family are suggested. Bayesian and maximum likelihood methods are employed to estimate the model parameters, and a Monte Carlo simulation evaluates the performance of the proposed bivariate family. Finally, the practical application of the proposed bivariate family is demonstrated through the analysis of four data sets.

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