[R] Equation au Fisher Law
Peter Dalgaard BSA
p.dalgaard at biostat.ku.dk
Wed Apr 9 16:59:03 CEST 2003
Thomas W Blackwell <tblackw at umich.edu> writes:
> Let X be the ratio of independent chi-squared random variables
> having k1 and k2 degrees of freedom. (k1 = numerator, k2 = denominator).
> Then X has density ... (this will take three lines to type out)
>
> dF(X) = [ Gamma((k1 + k2)/2) / (Gamma(k1/2) * Gamma(k2/2)) ]
>
> * (k1/k2)^(k1/2) * X^((k1/2) - 1)
>
> * (1 + X * (k1/k2))^-((k1 + k2)/2) * dX
>
> My source is:
> Samuel S. Wilks. Mathematical Statistics.
> Wiley, 1962. equation (7.8.9), p. 186. q.v.
>
> Probably Google would turn up the same result.
Not to mention ?FDist... Looks better when printed via LaTeX or in
the PDF version of the reference manual, though. To be specific, p.
213 of
http://cran.r-project.org/doc/manuals/refman.pdf
--
O__ ---- Peter Dalgaard Blegdamsvej 3
c/ /'_ --- Dept. of Biostatistics 2200 Cph. N
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
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