Uncertainty from normal distribution

Question

I'm working on Franck–Hertz experiment for labs at my university. My professor suggested using normal distribution to find the two maxima of function I(U) (see figure below).

I did fine with finding the maxima obtaining the following parameters for normal distribution for one of them:
$$mu=54.7712  [52.6229, 56.9195] $$
$$sigma=4.59029  [3.49087, 6.70445] $$
The intervals next to the parameter estimates are the 95% confidence intervals for the distribution parameters.
So $mu$ is my maximum point but how do I find its uncertainty? Is it $sigma$? Or do I need to do something with the intervals? I've never used this method and I'm confused.

Codename 47 · Accepted Answer

The short answer is that $mu$ is the center and $sigma$ is the width of the Gaussian curve which you are fitting. Thus, $sigma$ has nothing to do with the estimate of the peak.
Rather, since you have provided incomplete data, MatLab has done its best to guess how a fitted Gaussian would look. It has provided you with confidence intervals, and the easy solution is to just say that with 95% confidence you have $mu = 54.77 pm 2.15$, depending on how many significant digits you want. If you add / subtract the uncertainty you get the endpoints of the interval MatLab gave you.
To better clear up your confusion, you should take a look at how MatLab calculates that interval and try to understand where it comes from.
Also, while the normal distribution and the Gaussian curve are related, it is not entirely accurate to say you fit a normal distribution here. The data points are not a statistical distribution but a plot of a function.

Uncertainty from normal distribution

One Answer

Add your own answers!

Ask a Question