Bioinformatics and Information Science Center

Dr. Maochao Xu, Illinois State University

Linear combination of random variables has found wide applications in many areas such as statistics, queuing theory, actuary science, reliability theory, and communications, etc. For example, in reliability theory, it arises as the lifetime of a redundant standby system; in queuing theory, it is used to model the total service time by an agent in a system; in actuary science, it is used to model total claims on a number of policies in the individual risk model. In this talk, we focus on the analysis of efficiency, peakedness, majorization properties of linear combinations of random variables with light tail or heavy tail properties. Some related results in the literature will be studied in a unified framework.  Applications in statistical inference, actuary science, and reliability theory will be highlighted as well.