Hi @ldhubbert,
thank you for your question.
So firstly I would check again your skewed normal distribution definition, maybe this post could be useful for you: Clarifying a user defined function (skewed gaussian) (you can make use of the existing ROOT “gauss” function to make it simpler and avoid potential mistakes).
Secondly, it might also be easier to write ROOT macros instead of the C++ application that you need to compile as well, see: A ROOT Guide For Beginners.
Cheers,
Marta