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Exact distribution of product of generalized F ‐variates
Author(s) -
Shah M.C.,
Rathie P.N.
Publication year - 1974
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314970
Subject(s) - mathematics , cauchy distribution , function (biology) , random variable , product (mathematics) , riemann zeta function , distribution (mathematics) , pure mathematics , calculus (dental) , mathematical analysis , statistics , geometry , medicine , dentistry , evolutionary biology , biology
Abstract In this paper the exact distributions of products of independent generalized Snedecor's F ‐variables have been established in H ‐function, G ‐function, and in computable form. The exact distributions of products of independent F ‐variables, folded Student‐ t variables, beta second kind and folded Cauchy variables have also been obtained as particular cases. One particular case is verified with the result available in the literature. Calculus of residues, properties of Meijer's G ‐function, Psi function, H ‐function and Zeta function are used in deriving the results. Percentage points can be computed directly from the representation given in this article.