Histogram average gives wrong error

[NGoetz]

The average function of Histogram is "grob falsch". The standard error is not calculated correctly. I would replace this function by calling average_weighted with unit weights (DRY!). We should investigate why this was not caught by tests.

[NGoetz]

The reason why the tests let that through is because we only check for the value, but not the error in the test for average. This is sad. Additionally, average_weighted is never tested as far as I can see.

[Hendrik1704]

You mean this: self.error_ = np.sqrt(np.sum(self.histograms_, axis=0) / self.number_of_histograms_) is wrong? This is just the $\sqrt{N}$ of the averaged histograms assuming Poissonian statistics if I'm right.

[NGoetz]

I would have assumed to get the standard error just like for the average_weighted. The documentation claims that too. If we want a Poisson distributed error, that should be an optional argument, for both functions, and independently tested.

[Hendrik1704]

The standard deviation for Poissonian statistics is $\sigma= \sqrt{N}$, so this statement is correct, at least for a single histogram.

[NGoetz]

It's correct for Poissonian, but the documentation says standard error. Isn't standard error also a more reasonable default?

[Hendrik1704]

We should discuss with the others on Monday, what we want to put as a default.

[NGoetz]

I agree. An additional idea would be to add the option of error weighted average for weighted average right out of the box.

[NGoetz]

I think the standard error in the average_weighted is not even the standard error tbh. there is a factor missing.

[NGoetz]

raw_count is also not updated...? Bug or feature?