I have some data that are drawn from a Gaussian distribution with mean = 0 and std = 1. I then took each datum and squared it. The histograms below show a Gaussian distribution in black and the new squared data in red:
I am told that the new red distribution is a noncentral chi-squared distribution with 1 degree of freedom (parameter k=1) and parameter $\lambda$ I think should just be the square of the mean of the new red data (which seems to be very close to 1).
Therefore I am plotting a noncentral chi-squared distribution function over my histogram with k = 1 and $\lambda=1$. I did this in python using the scipy.stats.ncx2 package:
As you can see, it doesn't look to quite fit correctly. I wondered if anyone can spot if I am using the incorrect parameters or if there's something else that I'm doing wrong. I tried to vary $\lambda$ a little but that didn't seem to help. Is a noncentral chi-squared distribution the correct one to use?