Talk:Proofs related to chi-squared distribution

I thought the derivation of the distribution for k degrees of freedom a bit confusing. There's a clearer (in my opinion) derivation here:

http://scholar.lib.vt.edu/theses/available/etd-080399-001630/unrestricted/10Apxb.pdf

Basically: 1. We can easily derive the probability distribution of X^2 if X is N(0, 1).

2. Finding the pdf of the sum from i=1 to k of the (X_i)^2 requires us to convolve their probability distributions.

3. We can easily do these k-convolutions by just taking the characteristic function of the probability distribution of X^2, and raising it to the kth power (as multiplication in the characteristic function space is equivalent to convolution in the pdf space).

4. Then you just take the inverse transform of this new characteristic function, and you're done. No magical algebra or jacobians...

I'd add this in, but I'm not great with Latex yet.

Potnisanish (talk) 15:22, 4 February 2015 (UTC)

The derivation may be more efficiently done by working on the moment generating function of the sum of squares of the standard normal variables. 103.53.59.50 (talk) 06:43, 16 February 2023 (UTC)