# Find the underlying normal distribution of a folded normal distribution

This might be a very basic question, but I haven't found a clear answer anywhere, so I hope someone here can help.

How does one find the mean and standard deviation of a normal distribution that underlies a folded normal distribution?

In other words, if you have data that follows a folded normal distribution but want to "unfold" it, calculate the mean and stdev of the unfolded distribution, how do you go about it?

To go by an image (from Wikipedia). I have the green curve, but want the purple line:

Is it simply the mean and stdev from the folded normal equation, as described here?

Or is it this equation?

Cheers!

• – J.G. Mar 23 at 22:19
• That's all right, I have the gradient ascent coded already. I just wasn't sure if it was correct. So, the mean and sigma in the folded norm equation are the mean and sigma of the underlying normal? It that's the case, partial derivatives of the equation in respect to those two parameters as they are in the section of wiki you linked are what I need (just need to iterate until they approach zero) - correct? – David Mar 24 at 6:38
• Correct. A function of an $N(\mu,\,\sigma^2)$ variable uses those parameter symbols even if neither the mean nor the variance is the same as in the original variable. Lognormal variables are an example. – J.G. Mar 24 at 6:58