Could not find equation of function from data

Question

I have a problem to find equation of function of my data:

0.00 0.007

0.20 0.041

0.40 0.165

0.60 0.449

0.80 0.816

1.00 0.982

1.20 0.741

1.40 0.212

1.60 -0.362

1.80 -0.808

2.00 -0.975

2.20 -0.774

2.40 -0.290

2.60 0.290

2.80 0.775

3.00 0.982

3.20 0.849

3.40 0.527

3.60 0.237

3.80 0.077

4.00 0.018

4.20 0.003

4.40 0.002

4.60 0.001

4.80 0.001

5.00 0.001

The shape of curve is on image.

I suggest that there are three extreme, and two radix x1 and x2.

I need this shape to make an optimalization of function data, but I don´t know the shape of equation to fit the parameter of function.

Does anyone know some way around this?

Thanks

Paul!

Answer 1

Adjusting the four parameters of the function $$f(r,a,b,c):=-\left(a-b\,(x-r)^4\right)\;e^{-c\,(x-r)^2}$$ ($b\,(x-r)^2$ seemed too weak) I obtained for $f(2.02,1,12,2.4)$ :

Still not perfect but it may provide additional inspiration!