Penaksiran Parameter Distribusi Weibull Menggunakan Maksimum Likelihood dan Ant Colony Optimization

Abstract

Maximum Likelihood is a commonly used statistical method to estimate the parameters of probabilistic models. Ant Colony Optimization is a heuristic method that performs search in optimization using a system of approximations. This study uses Maximum Likelihood and Ant Colony Optimization to estimate and test the parameters of the Weibull distribution. The distribution used to estimate the parameters is the two-parameter Weibull distribution. Maximum Likelihood has the ability to produce efficient and consistent estimates in many cases. This method forms a likelihood function, which is the product of the probability density functions for each data point. Then, this likelihood function is converted to log-likelihood for ease of calculation. Furthermore, the parameter value that maximizes this log-likelihood is considered as the estimator. Ant Colony Optimization (ACO) is influenced by parameter values so that it can produce solutions that are close to optimal or even optimal. Testing is done with several trials so as to produce the best parameter values. When run, the path formation of each ant in the Ant Colony Optimization (ACO) algorithm is designed based on its probability value, where the system will recommend a different path when the results are not optimal or close to optimal. Based on the estimators obtained from data simulations using Python programming, it is found that the estimation of the Weibull distribution parameters using Maximum Likelihood is well used in the Weibull distribution based on the Fitness value.