國立政治大學統計學系
學 術 演 講
主講人：蘇南誠教授 (臺北大學統計學系系主任)學 術 演 講
題 目：Skew-Normal Distributions: Theory, Sampling Properties, and Applications
時 間：民國114年3月24日 (星期一) 下午1：30
地 點：國立政治大學逸仙樓050101教室
摘 要：
The skew-normal distribution generalizes the normal distribution while retaining many of its key properties. This talk begins with an overview of its fundamental characteristics and related research. We then examine the sampling distribution of a skew-normal population, including explicit forms of the probability density function, cumulative distribution function of the sample mean, and the joint moment generating function of the sample mean and variance. Additionally, we explore the distribution of linear combinations of independent but not necessarily identically distributed Azzalini’s skew-normal variables, deriving their exact probability density and cumulative distribution functions. These findings have practical applications in control charts and diagnostic testing, particularly in improving ROC curve analysis for skewed data, though computational challenges remain.
Keywords：Area under ROC curve, EWMA, diagnostic testing, two-stage control chart, skew-normal distribution