A NUMERICAL SOLUTION OF THE PROBLEM OF MOMENTS
成果类型：
Article
署名作者：
HARTLEY, HO; KHAMIS, SH
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
发表日期：
1947
页码：
340351
关键词：
摘要：
Many statistics have sampling distributions which are not easily evaluated numerically. If it is possible to find simple formulae for the moments, the distributions may be approx. evaluated in a simple way. When R moments are known, the effective range is subdivided into (R + 1) intervals and the moments (plus Sheppard''s corrections) expressed as linear combinations of the frequencies. Since the matrix of the system of equations is non-zero, the unknown frequencies are then obtained from the inverse matrix and the known moments. The matrix for the system involving R moments is standardized so that only one inverse need be calculated. Interpolation is facilitated by making calculations for several grids and combining the results into a single table. Examples are given of the calculation for an incomplete B-function, a [chi]-distribution, the normal function and a t-distribution.