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

DOI10.2307/3315037zbMath0596.62017OpenAlexW1989959924MaRDI QIDQ3729810

Serge B. Provost

Publication date: 1986

Published in: Canadian Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/3315037

zbMATH Keywords

linear combinationMeijer's G-functioninverse Mellin transformexact densityLauricella hypergeometric functionsindependent chi-square variables

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Exact distribution theory in statistics (62E15) Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60)

Related Items (8)

Moments of the product and ratio of two correlated chi-square variables ⋮ The residual effect of a growth‐decay mechanism and the distributions of covariance structures ⋮ On linear functions of certain noncentral versions of independent gamma variables ⋮ On the Ratios of Pathway Random Variables ⋮ Equivalent conditions for noncentral generalized Laplacianness and independence of matrix quadratic forms ⋮ Generalized Hypergeometric Functions and Exact Distributions of Test Statistics ⋮ On sums of independent gamma eandom yariames ⋮ Distribution of products of independently distributed pathway random variables

Cites Work

• The exact non-central distribution of the generalized variance
• Tests for change of parameter at unknown times and distributions of some related functionals on Brownian motion
• Content of the frustum of a simplex
• Further results on the trace of a noncentral wishart matrix
• Moments of the trace of a noncentral wishart matrix
• Confidence Region for a Linear Relation
• The Distribution of the Generalized Variance
• Probability Content of Regions Under Spherical Normal Distributions, IV: The Distribution of Homogeneous and Non-Homogeneous Quadratic Functions of Normal Variables
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