Understanding the importance of goodness of fit tests in univariate distribution: A systematic literature review

Univariate distribution is a crucial aspect of inferential statistics involving a single variable. The Goodness of Fit (GoF) test is a method used to evaluate how well a specific statistical model fits the observed data. This study aims to explore the importance of GoF tests in the context of univariate probability distributions and to identify methods and techniques that can enhance the accuracy of GoF testing. This research employs a systematic literature review (SLR) method, involving a literature search from 2015 to 2024 in databases such as Cambridge, Elsevier, IEEE, Springer, Taylor & Francis, and Wiley. A total of 87 articles were selected and assessed based on inclusion and exclusion criteria. The analysis focused on commonly used GoF methods such as Kolmogorov-Smirnov, Anderson-Darling, Cramer-von Mises, Jarque Bera, and Chi-Square, as well as parameter estimation and clustering techniques. The main findings highlight the importance of GoF tests in evaluating the fit of probability distributions with empirical data. The most frequently used GoF methods include Kolmogorov-Smirnov, Anderson-Darling, and Cramer-von Mises. Parameter estimation techniques such as maximum likelihood and the method of moments, as well as clustering techniques like k-means and hierarchical clustering, are proposed to improve the accuracy of GoF testing. The optimal cluster evaluation was conducted using the Calinski Harabasz, Davies Bouldin, and Silhouette methods. GoF tests are essential for validating statistical analysis results and making reliable inferences. The use of parameter estimation and clustering techniques can enhance the accuracy and effectiveness of GoF tests in univariate probability distributions. This research provides a strong foundation for further studies in this field.