- #1

Grogs

- 151

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**I need to fit a tail-heavy "Gaussian" curve**

Hi, it's been a long time since I've been around PF.

## Homework Statement

This isn't a homework problem per se, but I've been trying to fit some scattering data using a Gaussian function using a least squares approach and it's not working so well. Doing the fit is no problem, but the Gaussian doesn't follow the data very well. The agreement is good within ~ 1.5 standard deviation from the mean, but the data is too tail heavy and the agreement is lousy beyond that.

I need to find a function that will fit the data better. Something with a scaling parameter that would let me vary the kurtosis (tail heaviness) would be ideal, but I can't think of anything that fits the bill. I'm hoping that there's a stats whiz around who can point me in the right direction.

## Homework Equations

My Gaussian fit function: [itex]f(\theta) = Aexp(-\theta^{2}/2s^{2})[/itex] where A and s are the fit parameters (mean = 0).

I also tried using: [itex]f(\theta) = B + Aexp(-\theta^{2}/2s^{2})[/itex]

## The Attempt at a Solution

I tried adding a constant to the Gaussian fit, but then the fit ends up being too large at the tails.

TIA,

Grogs