An integral which occurs in statistics
Author:
- A. E. InghamAIA. E. Ingham
- 1 May 1933
- journal article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 29 (2) , 271-276
Abstract
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 equationKeywords
This publication has 2 references indexed in Scilit:
- The generalised product moment distribution in a normal systemMathematical Proceedings of the Cambridge Philosophical Society, 1933
- THE GENERALISED PRODUCT MOMENT DISTRIBUTION IN SAMPLES FROM A NORMAL MULTIVARIATE POPULATIONBiometrika, 1928