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Math Help - find g(X) that transforms folded normal into gamma(alpha,beta)

  1. #1
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    Smile find g(X) that transforms folded normal into gamma(alpha,beta)

    Hi, I got stuck with the question 3.20 b) in casella and berger 2nd (no solution for this question in the pdf solution manual)

    The question ask u to find the transformation Y=g(X) and the values of alpha and beta that transforms the folded normal into gamma(alpha,beta)
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  2. #2
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    If x~folded normal(0,1), then y = sum{i=1 to k} x^2 ~ chi-square(k), where k = d.o.f.

    Because the chi-square(k) is a special case of the gamma(a,b) where a = k/2 and b = 1/2.

    Thus, given x~folded normal(0,1), g(x) = sum{i=1 to 2a} x^2 ~ gamma(a,1/2).

    Hope it helps!!

    Traxex, Iesiadot
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