Employing the genetic algorithm to estimate the bivariate Weibull Distribution parameters and comparing it with the CME method

The Bivariate Weibull Distribution (BVD) is widely used in reliability analysis to model dependent failures. Due to its complexity, parameter estimation poses significant challenges. This study applies Maximum Likelihood Estimation (MLE), Correlation-Based Estimation (CME), a Genetic Algorithm (GA) approach, and the Pseudo Maximum Likelihood Estimator (PMLE), all implemented in R. PMLE is introduced as a practical alternative when the full joint likelihood is analytically intractable, offering estimation based on simplified marginal components. Performance was evaluated using both simulated data (500 iterations, sample sizes 100 and 150). Results based on mean squared error (MSE) show that GA consistently outperforms MLE, CME, and PMLE, particularly in estimating shape, scale, and dependence parameters. GA proves to be a robust alternative for complex models, and future work may focus on hybridizing GA with MLE for improved estimation accuracy. The real-world data from the air quality dataset, modeling wind-speed and temperature dependence, further supports the theoretical model. The combined behavior of temperature and wind speed is well captured by the bivariate Weibull distribution, which is further strengthened by an interaction term controlled by θ. The model's ability to explain dependent data from the actual world is validated by the fitted parameters, which offer significant insight into the nature of atmospheric variability