訂正日: 2006/08/29訂正理由: -訂正箇所: 論文タイトル訂正内容: Wrong : on the characteriation of the normal population by the independence of the sample mean and the sample variance Right : On the characterisation of the normal population by the independence of the sample mean and the sample variance
訂正日: 2006/08/29訂正理由: -訂正箇所: 引用文献情報訂正内容: Right : (1) R. C. Geary, The distribution of “Student's” ratio for non-normal samples. Journ. Royal Statist. Soc., Supplement 3 (1936). (2) R. A. Fisher, Moments and product moments of sampling distributions. Proc. London Math. Soc. 30 (1929). (3) In the ordinary sense of the characteristic function, t, s are real, but in this paper, we use the same terminology in the case where s is complex. (4) The dash in α'(s) means the differentiation with respect to s. (5) This can also be proved explicitly. From the existence of lim αn we can show that the variance of Z is finite, and 1/i lim τ→0 α'(iτ)=E(Z), the mean value of Z, which is (n-1)σ2, σ2 being the variance of Xi. This is a well known fact in the sampling theory. Hence αn is independent of n. For βn, we can also prove its independence of n directly.
