# Get the number of counts from a Gaussian that fits the logarithm of counts

I have n data to fit: $$x=[\text{channel}_1,\text{channel}_2,\dots,\text{channel}_n]$$ $$y=[\ln(\text{count}_{1}),\ln(\text{count}_{2}), \dots,\ln(\text{count}_{n})]$$ I'm considering a spectral peak which I'm fitting with a gaussian. $$\ \ln[\text{counts}(x)] = \frac{N} {\sigma\sqrt{2\pi}} e^{-(x-\mu)^2/(2\sigma^2)} \,.$$ So I obtained the parameters $$N,\mu,\sigma$$. I want to estimate all the counts under the peak, but N now is not the number I'm looking for because there is the logarithm transformation.

• I don't know how to do, maybe I have to solve the integral: $$\int_{-\infty}^{\infty}\exp\left[\frac{N} {\sigma\sqrt{2\pi}} e^{-(x-\mu)^2/(2\sigma^2)} \right]\,\mathrm{d}x= ?$$

Can I do some operations directly on N?

• Don't see any obvious way of estimating the total counts under the peak or calculating the function of N and $\sigma$ shown on the left side of your last equation. Think that you would just have to use numerical integration to calculate that function after each time you do a peak fit. If you have a lot of peaks to deal with, it might be faster to first generate a look-up table for g[N,$\sigma$], where g is the function of N and $\sigma$ on the left side of the last equation. – Samuel Weir Sep 23 at 21:47