Take the 2-minute tour ×
Mathematica Stack Exchange is a question and answer site for users of Mathematica. It's 100% free, no registration required.

I tried to substitue variable x of one equation with another variable z (z=nx/(nx+m)). See as follow:

Solve[z == n*x/(n*x + m), x]
x -> -((m z)/(n (-1 + z)))

Then:

PDF[FRatioDistribution[n, m], x] /. x -> -((m z)/(n (-1 + z)))
 (m^(m/2) n^(n/2) (-((m z)/(n (-1 + z))))^(-1 + n/2) (m - (m z)/(-1 + z))^(1/2 
  (-m - n)))/Beta[n/2, m/2]

How can I collect the term z and 1-z together? Factually, if collecting the results by `z and1-z`, it can be very simple (that is Beta distribution). Any suggestion will be greatly appreciated.

share|improve this question
1  
Just FullSimplify[..., Assumptions -> {n > 0, m > 0}] –  ybeltukov Oct 13 '13 at 22:05
    
Thaks your reply. it helps. –  user2069518 Oct 14 '13 at 5:13
    
@ybeltukov answer? –  Yves Klett Oct 14 '13 at 17:45
add comment

1 Answer

FullSimplify with Assumptions makes what you want

FullSimplify[PDF[FRatioDistribution[n, m], x] /. x -> -((m z)/(n (-1 + z))), 
  Assumptions -> {n > 0, m > 0}]
(n (1 - z)^(1 + m/2) z^(-1 + n/2))/(m Beta[n/2, m/2])
share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.