# Bell-curve shape regression [duplicate]

I am trying to fit some data that looks like a bell-curve: we reach a maximum at some value close to the mean, then the graph falls towards zero as we get further away from it. I am not the "owner" of the data so I cannot share it with you here, but I think the idea is clear with the "fake data" below

I would like to find a non-linear model that can fit that type of data, but my search did not give me much information. What are your suggestions?

• Have you tried a regular linear model already? How were the residuals? Also, is your real data also bounded in 0 and 1000? – user2974951 Aug 30 '19 at 9:39
• @user2974951 The data is in principle not bounded, but we would get all zeros if we go too much beyond. A regular linear model does not work here as there is no upward/downward trend – David Aug 30 '19 at 9:49
• @David If you have other variables try a regular linear model first and check the residuals. If this is all the data that you have then, as mkt suggested, try a GAM model. – user2974951 Aug 30 '19 at 10:01
• @user2974951 There are no other predictors. All the data is plotted there – David Aug 30 '19 at 10:03
• – gung - Reinstate Monica Aug 30 '19 at 12:05

• What would you do if, for instance you knew $y=f(x)$ where $f$ follows the shape of a normal-distribution density function? – David Aug 30 '19 at 11:56