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.