Comparison of Metaheuristic Algorithms for Maximum Likelihood Estimation of the Transmuted Weibull Distribution with Applications

The Weibull distribution, widely utilized due to its flexibility, often requires generalization to improve its fit to real-world data. The Transmuted Weibull Distribution offers enhanced flexibility by incorporating a transmutation parameter. Metaheuristic algorithms have emerged as robust tools for parameter estimation, particularly for probability distributions with complex likelihood functions. This study compares the performance of four metaheuristic algorithms: Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), and Artificial Bee Colony (ABC) against the traditional Newton-Raphson (NR) algorithm for estimating parameters of the Transmuted Weibull Distribution (TWD). Extensive Monte Carlo simulations evaluated the algorithms' efficiencies using metrics like log-likelihood values, bias, mean squared error (MSE), and deficiency. Additionally, the methods are applied to real-world datasets to compare their practical utility. Both simulation and real data application results revealed that metaheuristic algorithms outperformed traditional Newton-Raphson (NR) optimization.