Maximum Likelihood Estimation for the Log-Logistic Distribution Using Whale Optimization Algorithm with Applications

The log-logistic distribution has been widely used in several fields, including engineering, survival analysis, and economics. The method of maximum likelihood estimation is used in this study for estimating the shape and scale parameters for the log-logistic distribution, whereas in the case of the log-logistic distribution, likelihood equations lack explicit solutions. Therefore, problems with solving likelihood equations can be solved by using two highly efficient algorithms, which are the whale optimization algorithm and the Nelder-Mead algorithm, as well as by showing the applicability of this distribution by comparing it with other well-known classical distributions. To demonstrate the performance of each algorithm implemented, an extensive Monte Carlo simulation study has been conducted. The performance of maximum likelihood estimators for each algorithm has been evaluated in terms of mean square error and deficiency criteria. It has been seen that the whale optimization algorithm provides the best estimates for the log-logistic distribution parameters according to the simulation data.