A NOTE ON THE ASYMPTOTIC DISTRIBUTION OF RANGE
成果类型：
Article
署名作者：
COX, DR
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
发表日期：
1948
页码：
310315
关键词：
摘要：
Three asymptotic distributions, one of which is new, are discussed for the case of samples from a symmetric unimodal distribution. Gumbel''s distribution (Ann. Math. Stat., 1947), in terms of a modified Bessel function of the second kind appears to be least accurate. Cox''s distribution is of the form [image] where [PHI] (x) and [PHI] (x) are the frequency and distribution functions of the basic symmetrical distribution with mean zero, and wn is the sample range. This distribution is obtained by the method of steepest descents and is somewhat more accurate than the first but not quite as accurate as Elfving''s approximation (Biometrika, 1947) to the distribution of a non-linear function of the sample range as a first order Bessel function. However, the non-linearity of Elfving''s transformation makes his method less useful algebraically.