A0374
Title: A study on the distribution of the sum of independent but not necessarily identical skew-normal random variables
Authors: Nan-Cheng Su - National Taipei University (Taiwan) [presenting]
Abstract: The focus is on the distribution of linear combinations of independent but not necessarily identically distributed Azzalinis skew-normal random variables. Their exact probability density function and cumulative distribution function are derived, extending prior results in the literature. These findings have been applied to several areas, including developing EWMA control charts designed to handle skewed data, aiming to improve process monitoring efficiency. Theoretical support for evaluating diagnostic tests is also provided, particularly in scenarios where experimental and control group data follow skew-normal distributions, enhancing the reliability of the ROC curve and AUC calculations. Additionally, this research contributes to the theoretical framework for two-stage control charts tailored to processes involving skewed data. However, these applications still face challenges due to the computational complexity of numerical solutions.
