[R] Equation au Fisher Law

[Peter Dalgaard BSA]

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