Comparison of some estimation methods for fuzzy reliability function and parameters of the transformed kappa model with practical application

Abstract

In this research, we conduct an experimental statistical analysis using simulation and real-life application on unusual life data characterized by fuzziness. Specifically, we study the downtime of towers belonging to Zain Iraq Telecommunications Company, which are sometimes not recorded when they are repaired. We successfully handle and analyze this fuzzy data by proposing a distribution called "Alpha Power kappa" distribution. Which was built using a transformation formula called (Alpha Power Transformed). and derive the fundamental properties of the distribution, We estimate the parameters and reliability function using estimation methods such as maximum likelihood, Kremer-von Mises method, and method of moments. By comparing, the results obtained from the simulation experiment, using statistical criteria such as mean squared error (MSE), and integrated mean squared error (IMSE). We compare the performance of these estimation methods. We find that the maximum likelihood method is the best among these methods for estimation. Furthermore, by relying on statistical criteria such as Akaike information criterion (AIC), corrected Akaike information criterion (AICc), and Bayesian information criterion (BIC). We conclude that the proposed Alpha Power kappa distribution outperforms the original kappa distribution in representing real data.