In various types of statistical analysis, the Weibull distribution is an important continuous probability distribution. One crucial aspect of studying this distribution is estimating its parameters. The maximum likelihood method is the approach used for the two-parameter Weibull distribution. This method aims to determine the parameter values by maximizing the likelihood function based on the available data. The advantages of the maximum likelihood method lie in its properties, such as consistency, efficiency, and asymptotic normality. Since the form of the likelihood function in the Weibull distribution is quite complex and cannot be solved analytically, numerical solutions are required. One approach used is the Newton-Raphson method, which serves to approximate the parameter values or find the optimal solution.
