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Transforming F distribution into B distribution.

  1. Dec 1, 2009 #1
    1. The problem statement, all variables and given/known data

    Show that

    Y = 1 / [ 1 + (r1/r2)W ]

    where W has an F distribution with parameters r1 and r2 has a beta distribution.

    3. The attempt at a solution

    P(Y<or=y) = P(1 / [ 1 + (r1/r2)W ] <or = y) = P( W > (1/y - 1)(r2/r1)) = 1 - P(W<or= (1/y - 1)(r2/r1))...etc

    Then I use the known pdf of an F distributed variable and try to simplify it into the form of a beta distribution's pdf, but I get stuck in the simplification process. Is there an easier/better/more correct approach to this problem?

    Any hints would help!
     
  2. jcsd
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