Bivariate Chen distribution based on iterated FGM copula: Properties and applications

This paper introduced a bivariate model constructed by coupling the iterated Farlie-Gumbel-Morgenstern (IFGM) copula with Chen marginals, yielding the bivariate IFGM-Chen distribution (IFGM-CD). The model was particularly tailored for reliability and survival analysis, as it accommodated bathtub-shaped hazard rates and captured a broader spectrum of dependence structures than traditional FGM-based models. Fundamental statistical properties were investigated, including product moments, conditional distributions, and reliability functions. A dedicated section on the stress-strength model within the IFGM-CD framework was provided, offering new insights into component reliability under dependent stress and strength. For parameter estimation, both maximum likelihood (ML) and Bayesian approaches were employed, supplemented by asymptotic and bootstrap confidence intervals. Extensive Monte Carlo simulations validated the performance of the estimators, and two real-data applications demonstrated the model's practicality and flexibility.