Aplikasi Penalized Maximum Likelihood Estimation pada Distribusi Weibull dengan Algoritma Gradient Descent

Abstract

The Weibull distribution is widely used in reliability analysis and failure modeling due to its flexibility in modeling various types of data. For accurate parameter estimation, the Penalized Maximum Likelihood Estimation (PMLE) method with the Gradient Descent (GD) algorithm is applied to address overfitting and optimize the parameters of this distribution. This study implements PMLE on the Weibull distribution to achieve stabel parameter estimation, utilizing numerical methods like Gradient Descent (GD) since the resulting likelihood function often lacks a direct analytical solution. PMLE introduces a penalty to the likelihood function to control model complexity and prevent overfitting. Based on simulations conducted using Python, it was found that the estimation of the two-parameter Weibull distribution using PMLE with the GD algorithm is effective for this distribution. This is evidenced by the small bias values obtained. PMLE excels in producing stabel and consistent estimates, resulting in estimators that closely approximate the true parameter values. Therefore, PMLE is a more reliable method for estimating the parameters of the Weibull distribution, particularly for data with limited sample sizes.