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The exact distribution of the ratio of a linear combination of chi‐square variables over the root of a product of chi‐square variables

 

作者: Serge B. Provost,  

 

期刊: Canadian Journal of Statistics  （WILEY Available online 1986）
卷期: Volume 14, issue 1  

页码: 61-67

 

ISSN:0319-5724

 

年代: 1986

 

DOI:10.2307/3315037

 

出版商: Wiley‐Blackwell

 

关键词: Linear combinations;products and ratios of chi‐square variables;general linear model;multivariate linear functional relationships;exact distributions;approximations

 

数据来源: WILEY

 

摘要:

AbstractThis article gives the exact distribution of a statistic whose numerator and denominator are independent, the former being a linear combination of independent chi‐square variables and the latter being thekth root of a product ofkindependent chi‐square variables. This structure appears in the study of multivariate linear functional relationship models. The technique of the inverse Mellin transform is used in order to obtain the density of this test statistic in a computable f

 

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