A new extension of the FGM copula with an application in reliability

Ebaid, Rasha; Elbadawy, Walid; Ahmed, Essam A.; Abdel-Ghaly, Abdalla

doi:10.1080/03610926.2020.1785501

Cited by 7 publications

(8 citation statements)

References 15 publications

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“…Clearly, the Spearman's Rho and Kendall's Tau of the copula (2.1) can be determined by reversing the sign of b in ( 17) and ( 18) in Ebaid et al [17] as ρ = a(2+b) 2…”

Section: The Main Resultsmentioning

confidence: 99%

“…For more details about the Huang-Kotz copulas, see the recent works [1,12]. Ebaid et al [17] proposed the following new extended FGM copula…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, Ebaid et al [17] used the copula (1.7), with a wrong admissible range (cf. [10]), to estimate the reliability in a dependent stress-strength model with an application to the Egyptian finance system.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A more flexible counterpart of a Huang-Kotz's copula-type

Barakat¹,

Alawady²,

Husseiny³

et al. 2022

Preprint

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“…Clearly, the Spearman's Rho and Kendall's Tau of the copula (2.1) can be determined by reversing the sign of b in ( 17) and ( 18) in Ebaid et al [17] as ρ = a(2+b) 2…”

Section: The Main Resultsmentioning

confidence: 99%

“…For more details about the Huang-Kotz copulas, see the recent works [1,12]. Ebaid et al [17] proposed the following new extended FGM copula…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A more flexible counterpart of a Huang-Kotz's copula-type

Barakat¹,

Alawady²,

Husseiny³

et al. 2022

Preprint

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show abstract

“…Additionally, the first and second types of extensions given in [7] (designated by the abbreviations HK-FGM1 and HK-FGM2) offer a close correlation range. Barakat et al [8,9] amended a new symmetric generalization of FGM copula, which was introduced in [10] (this paper was published on the line in 2020).…”

Section: Introductionmentioning

confidence: 99%

Scrutiny of a More Flexible Counterpart of Huang–Kotz FGM’s Distributions in the Perspective of Some Information Measures

Abd Elgawad,

Barakat,

Abd El-Rahman

et al. 2023

Symmetry

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In this work, we reveal some distributional traits of concomitants of order statistics (COSs) arising from the extended Farlie–Gumbel–Morgenstern (FGM) bivariate distribution, which was developed and studied in recent work. The joint distribution and product moments of COSs for this family are discussed. Moreover, some useful recurrence relations between single and product moments of concomitants are obtained. In addition, the asymptotic behavior of the concomitant’s rank for order statistics (OSs) is studied. The information measures, differential entropy, Kullback–Leibler (KL) distance, Fisher information number (FIN), and cumulative past inaccuracy (CPI) are theoretically and numerically studied.

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“…For a comprehensive review of bivariate FGM copulas and their generalizations, we refer the reader to Bayramoglu, 2013, Saminger-Platz et al, 2021]. Some examples of these generalizations include [Huang and Kotz, 1984, Huang and Kotz, 1999, Lai and Xie, 2000, Bairamov and Kotz, 2002, Rodríguez-Lallena, 2004, Amblard and Girard, 2009, Kim et al, 2011, Durante et al, 2013, Pathak and Vellaisamy, 2016, Hürlimann, 2017, Komorník et al, 2017, Côté and Genest, 2019, Bekrizadeh, 2022, Ebaid et al, 2022. These copulas are usually constructed by validating the existence of the copula.…”

Section: Introductionmentioning

confidence: 99%

A new method to construct high-dimensional copulas with Bernoulli and Coxian-2 distributions

Blier-Wong¹,

Cossette²,

Legros³

et al. 2022

Preprint

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We propose an approach to construct a new family of generalized Farlie-Gumbel-Morgenstern (GFGM) copulas that naturally scales to high dimensions. A GFGM copula can model moderate positive and negative dependence, cover different types of asymmetries, and admits exact expressions for many quantities of interest such as measures of association or risk measures in actuarial science or quantitative risk management. More importantly, this paper presents a new method to construct high-dimensional copulas based on mixtures of power functions, and may be adapted to more general contexts to construct broader families of copulas. We construct a family of copulas through a stochastic representation based on multivariate Bernoulli distributions and Coxian-2 distributions. This paper will cover the construction of a GFGM copula, study its measures of multivariate association and dependence properties. We explain how to sample random vectors from the new family of copulas in high dimensions. Then, we study the bivariate case in detail and find that our construction leads to an asymmetric modified Huang-Kotz FGM copula. Finally, we study the exchangeable case and provide some insights into the most negative dependence structure within this new class of high-dimensional copulas.

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A new extension of the FGM copula with an application in reliability

Cited by 7 publications

References 15 publications

A more flexible counterpart of a Huang-Kotz's copula-type

A more flexible counterpart of a Huang-Kotz's copula-type

Scrutiny of a More Flexible Counterpart of Huang–Kotz FGM’s Distributions in the Perspective of Some Information Measures

A new method to construct high-dimensional copulas with Bernoulli and Coxian-2 distributions

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