Asymtotic Normality Of Order Statistics And Simple Linear Rank Statistics

Linear order statistic and linear rank statistic are two kinds of important statistics in the mathematical statistics. They are used widely and a lot of the other statistics belonging to them. In 1960's, the famous statist,named Moore, proved the asymptotic normality of one kind of linear order statistic. While Hajek gained the equational condition of the asymptotic normality of rank statistic. In this paper, we use the convex function to form the order statistic and the linear rank statistic, and the asymptotic normality of the statistics are proved.