Estimating Kappa Distribution Parameters: A Comparative Study of Maximum Likelihood and LQ-Moment Approaches

Abstract

The Kappa distribution, pioneered by researchers such as Hosking, stands as a widely applied continuous model in diverse scientific fields. This study delves into its practical utility, with a specific focus on amalgamating Gamma and Log-Normal distributions. The vital distributional parameters($\alpha ,\beta,\theta$)are subject to estimation through both Maximum Likelihood (MLE) and LQ-moment methods. Across a spectrum of sample sizes (25, 50,100, and 150), the LQ-moment method consistently exhibits superior performance compared to MLE.Additionally, the research introduces two essential reliability metrics: Mean Inactivity Time (MIT) and Stress-Strength Reliability (SSR). MIT, influenced by distribution parameters, provides insights into the temporal behavior of the random variable. SSR evaluates system reliability by accounting for the probability of component failure under stress conditions. The paper concludes with a comparative analysis of parameter estimation methods, emphasizing the enhanced accuracy of the LQ-moment approach, particularly noticeable in smaller sample sizes (50 and 100).