An integral which occurs in statistics
An integral which occurs in statistics
复制标题
统计中出现的积分
DOI：
10.1017/s0305004100011075
复制
发表时间：
1933
影响因子：
0.8
通讯作者：
A. E. Ingham
中科院分区：
文献类型：
--
作者：
A. E. Ingham
1.在这篇注记中，我们给出了一个积分的直接评估，其值已从统计理论推断。这里A = Ap =（αμν）和C = Cp =（Cμν）是真实的对称矩阵，其中A是正定的;有1/2 p（p + 1）个独立的积分变量tμν（1 ≤ μ ≤ ν ≤ p），为了符号的对称性，tμν也写作tνμ;在求和∑中，变量μ，ν独立地从1到p运行; k是真实的数。关于权力的确定，有必要作一点解释。|A − iT|- k。由于A是正定的，T是真实的且对称的，方程的根
1. In this note we give a direct evaluation of the integral whose value has been inferred from the theory of statistics. Here A = Ap = (αμν) and C = Cp = (Cμν) are real symmetrical matrices, of which A is positive definite; there are ½ p (p + 1) independent variables of integration tμν (1 ≤ μ ≤ ν ≤ p), and tμν is written also as tνμ for symmetry of notation; in the summation ∑ the variables μ, ν run independently from 1 to p; k is a real number. A word of explanation is necessary with regard to the determination of the power |A − iT|−k. Since A is positive definite and T real and symmetric, the roots of the equation