Wrote

Normal PDF almost don't exist in physics unless intentional
like shooting 100 times the target with the same gun.
Under the hood there may be Logistic, Weibull noise.
If you have these 3 data sets from raw experiment,
please: attach as collected, absolutely untouched.
Cheers ... Jean

So here it is. Two cases. I counted the first one in the very first examples. There, the three normal distributions are summed up. In the last example, the other case is that two normal distributions are summed up.

But, actually, the problem is solved.
Only the time for calculating each case is too long.

Wrote

You forgot to attach the untouched experimental data set.
That's the only thing I need in statistical work.

Why did I forget? Both sets of data are there.

Here with two normal distributions (the third one is not visible).


Here with three normal distributions.


In principle, it is still necessary to take into account that these are histograms.
This is given as X the middle of the column.
Initially, the column width is 20 units, then 40 is for X=180, then in the first case the width is 100, and the last column is 50.
In the second case, the last three columns are 50 each.

Wrote

Wrote

Problem is that we don't know what you are looking for.
Are you looking for the best fit to your data set ???
If so, minute job.
Please, don't hesitate ... Jean

Now only one question remains. Iterating through 9 parameters requires a lot of time. And the calculation is carried out with an accuracy that is superfluous for my purposes.
Sq and Sqmin are calculated with an accuracy of 15 decimal places. And I would have more than enough 8 or 9 digits after the decimal point.
This would significantly reduce the calculation time.
And here is the Pearson correlation coefficient I have 0.9999, whereas I would have more than enough 0.9

Here is your Sq and Sqmin calculations.
I have noticed Sqmin make a peak to lowest and rise again at some point.
I coded to find those points range within first iteration.
This is done by evaluating variables one by one, not all at one.
All iterations are taken under 5 seconds on my PC.
Please inform if this results are enough for you.

Regards

eng-min_rev_fast.pdf (617 KiB) downloaded 28 time(s).
eng-min_rev_fast.sm (40 KiB) downloaded 26 time(s).

A revised Sq and Sqmin calculations of previous.
All iterations are taken under 25 seconds on my PC.
Sqmin is dropped to 6x10^-6. And now I am out of ideas.
Please inform if this results are enough for you.

Regards

eng-min_rev_fast.pdf (671 KiB) downloaded 31 time(s).
eng-min_rev_fast.sm (47 KiB) downloaded 35 time(s).

Show Spoiler

Colleagues

Thank you very much
Apparently, we need to stop here - the calculation method has been worked out.

Once again-thank you very much