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