gaussian fitting to histogram

[excelaitin]

Dear All,

I am trying to fit guassian function to a histogram whose x axis is logarithm base 10. I have attached a image in the excel sheet how I expect it to look, however, I cannot obtain anything like that. I don't know what I am doing wrong. I will appreciate if somebody can explain me where I went wrong.

Thank you.

[MrShorty]

tl:dr -- it appears to me that you do not have a correct Gaussian function in column C. I expect that most of the solution is to get a correct Gaussian function in column C.

You say that you are trying to fit to a Gaussian function, but your formula in column 3 is a parabola y=a*(-(x-b)^2/2/c). Wikipedia (https://en.wikipedia.org/wiki/Gaussian_function ) notes that a Gaussian function is one with the general form y=a*exp(-(x-b)^2/2/c^2). It looks like you neglected to include the exp() function in column C.

Then, as noted, your x axis is really a logarithmic axis, so you need to substitute log(x) for x in the Gaussian function y=a*exp(-(log(x)-b)^2/2/c^2). I make that correction to column C.

Then, I want to see what my fit looks like, so I select your XY scatter chart and expand the source data range to include column C. Now I can see both the original data and my best fit curve.

I want to enter some reasonable guesses for a, b, and c. Wikipedia notes that a is the height of the peak, which looks like it should be 2500, so I enter 2500 for a. Wikipedia notes that b marks the horizontal position of the top of the peak, which looks like it should be at log(1E-5), so I enter -5 for b. I can see that 1 looks like a good guess for c, so I leave c unchanged.

If I want to further optimize the fit, I come up with a suitable objective function for my curve fit (least squares or rmsd or whatever I deem appropriate), the call Solver and tell it to optimize the objective function by changing a, b, and c.

Does that help?