DefinePK

Abstract

Let \(X_{j}\), \(j = 1, 2, \ldots, n\) be the independent and identically distributed random vectors which take the values on the unit circumference. Let \(S_{n}\) be the area of the convex polygon having \(X_{j}\) as vertices. The paper by Nagaev and Goldfield (1989) has proved the asymptotic normality of random variableSn. Our main aim is to show that the random variableSn can be represented as a sum of functions of uniform spacings. This allows us to apply known results related to uniform spacings for the analysis of \(S_n\).