On the type-B integral equation and the distribution of wilks statist for testing independence of several groups of variables
作者:
Jen Tang,
A.K. Gupta,
期刊:
Statistics
(Taylor Available online 1987)
卷期:
Volume 18,
issue 3
页码: 379-387
ISSN:0233-1888
年代: 1987
DOI:10.1080/02331888708802034
出版商: Akademie-Verlag
关键词: Mixture;weighted gamma functions;beta functions;convergence;recursive formulae
数据来源: Taylor
摘要:
In this paper, WILKS'type-B integral equation is solved in the general form of a series of beta functions and a series of weighted gamma functions as proposed by WALD and BROOKNER 1941. The coefficients in both representations can be obtained by explicit recurrence relartions, therefore the results solve many distributional problems and have the fewest computational difficulties of any representation that has surfaced to date. The radius of convergence of the second series representation is given, whereas the convergence property of the first series representation is given, whereas the convergence property of the first series representation was studied by WALD and Brookner. The exact null distributions of WILKS' statistic A for testing the independence of several groups of variables and of V = -log A are given. The coefficients in all the series representration can be computed recursilvely and hence can be obtained easily with the help of modern computatinal facilities
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