An Extension of the d-Variate FGM Copula with Application
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908526873411584 |
|---|---|
| author | Hamadou, Mous-Abou Longla, Martial |
| author_facet | Hamadou, Mous-Abou Longla, Martial |
| contents | We introduce an extended d-variate Farlie-Gumbel-Morgenstern (FGM) copula that incorporates additional parameters based on Legendre polynomials to enhance the representation of multivariate dependence structures. Within an i.i.d. framework, we derive closed-form estimators for these parameters and establish their unbiasedness, consistency, and asymptotic normality. A simulation study illustrates the finite-sample performance of the estimators. The model is applied to the Bearing dataset, previously studied by Ota and Kimura (2021) through a d-variate FGM copula and by Longla and Mous-Abou (2025) using an extended bivariate FGM copula. Our analysis shows that the classical d-variate FGM copula does not adequately represent the dependence in this dataset. Based on estimation results and model selection criteria, we propose a reduced version of the extended model as a more appropriate copula specification for the Bearing data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07281 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Extension of the d-Variate FGM Copula with Application Hamadou, Mous-Abou Longla, Martial Methodology Applications 62H05, 62P30 We introduce an extended d-variate Farlie-Gumbel-Morgenstern (FGM) copula that incorporates additional parameters based on Legendre polynomials to enhance the representation of multivariate dependence structures. Within an i.i.d. framework, we derive closed-form estimators for these parameters and establish their unbiasedness, consistency, and asymptotic normality. A simulation study illustrates the finite-sample performance of the estimators. The model is applied to the Bearing dataset, previously studied by Ota and Kimura (2021) through a d-variate FGM copula and by Longla and Mous-Abou (2025) using an extended bivariate FGM copula. Our analysis shows that the classical d-variate FGM copula does not adequately represent the dependence in this dataset. Based on estimation results and model selection criteria, we propose a reduced version of the extended model as a more appropriate copula specification for the Bearing data. |
| title | An Extension of the d-Variate FGM Copula with Application |
| topic | Methodology Applications 62H05, 62P30 |
| url | https://arxiv.org/abs/2509.07281 |