Hi all,
I'm trying to find the one sigma limits for a particular probability distribution (see image). I don't have a functional form of the distribution-it's generated from discrete data points-although I think I could find a reasonable match using cftool.
What I would like to do is find the 1 sigma limits (68.2% of the prob) by using an iterative process that moves a line down the probability axis until it intersects the curve at two points that contain 68.2% of the area between them. In short, the idea would be to adjust the horizontal black line until the red area is the desired 68.2% of the total area under the curve. Apologies for the crummy drawing.
I have absolutely no clue where to start, besides coming up with a fit to the data. I would like to make it an iterative process where I input a starting height for the horizontal line and it 'homes' in on the proper height (to within some range).
A little nudge in the right direction would be great.
Side note: I'm pretty sure this is a known technique, but I don't know what it's called. If anyone knows the answer that would be a great start.
Best Answer