Say I have a data point with included errors and I want to build some continuous distribution around it. Normally this might be a Gaussian because one knows the sigma and mean right off the bat. However, if you have asymmetric errors it becomes a lot harder. It seems like you should be able to model a Gaussian about a data point with such errors using a skewed normal distribution, let me know if I am wrong.
Essentially, I would like to know if there is a way to generate a standard normal distribution if you know the mean, max, and min? The mean being the data point, max being the data point plus the upper bound, and min being the data point minus the lower bound.