Statistical Inference for a Novel Farlie-Gumbel-Morgenstern Copula-Based Bivariate Odd Rayleigh-Exponential Distribution

Abstract

This study develops a novel bivariate odd Rayleigh-exponential distribution (OR-ED), constructed using the Farlie-Gumbel-Morgenstern (FGM) copula to model dependence between lifetime data. Three estimation methods: maximum likelihood estimation (MLE), inference functions for margins (IFM), and canonical maximum likelihood (CML) are employed to evaluate model performance. Through extensive simulations, all estimators are shown to be consistent, with MLE providing the most accurate estimates and IFM offering a computationally efficient alternative. Practical applications to three real-life datasets demonstrate the flexibility and stability of the proposed model, achieving low biases and RMSEs across the board. The results highlight the model’s suitability for capturing moderate dependence in survival and reliability data, establishing the FGM copula-based OR-ED as an adaptable and efficient tool for joint lifetime analysis.

Keywords

bivariate lifetime data / dependence modelling / farlie-gumbel-morgenstern copula / inference functions for margins / maximum likelihood estimation / odd rayleigh-exponential distribution

Author Contributions

O.O., M.T., and I.A.S.: conceptualization; O.O., M.T., A.U., A.Y., and I.A.S.: methodology; O.O., M.T., and A.Y.: data curation; O.O. and M.T.: writing—original draft preparation; O.O., M.T., A.U., A.Y., and I.A.S.: visualization, investigation; M.T., A.U., A.Y., and I.A.S.: supervision; O.O., M.T., I.A.S., A.U., and A.Y.: software, validation; O.O., M.T., A.U., A.Y., and I.A.S.: writing—reviewing and editing. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the Tertiary Education Trust Fund (TETFund), Nigeria.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

Use of AI and AI-Assisted Technologies

During the preparation of this work, the authors used OpenAI/ChatGPT and Grammarly to improve clarity and language refinement. After using these tools/services, the authors reviewed and edited the content as needed and take full responsibility for the content of the published article.

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