[G12] Moments analysis - Entries + Errors

[Saini, Mukesh]

Hello All,

Yesterday, I could not explain exactly how I got the number of entries printed above the Individual Moment histogram. I initially said it was a sum of the events in the bins of the histograms, but then there were few histograms for which it should have been negative as Dennis pointed out.

I am better able to explain if you follow the process of the way I calculate the moments and the associated errors.

1. I calculate the Big-D function value for each event for different J,M,N and save those in an ntuple.

2. I histogram in 2D the D-Function vs Mass_kk

3. I take the X-Profile of this plot. This step is 'crucial'. This gives me the mean of the D-function and the associated error with it for a particular mass_kk bin. As per root page on TProfile:

http://root.cern.ch/root/html/TProfile.html

"Profile histograms are used to display the mean
value of Y and its error for each bin in X.
The displayed error is by default the
standard error on the mean (i.e. the
standard deviation divided by the sqrt(n) )"

I now have a histogram that displays the sum-average (mean) of a given D-Function for a given mass bin and has the correctly calculated standard errors associated with it.

4. Then I multiply the mass_kk histogram with the Dval_JMN_ProfileX histogram to arrive at the Corresponding Moments. This can also be understood as weighing the D-Function Sum-Average value for a given bin by the number of events in that particular mass-bin.

Relevant Plots to check:

http://hadron.physics.fsu.edu/~mukesh/files/pKKExc/PNG/mass_kk.png<http://hadron.physics.fsu.edu/%7Emukesh/files/pKKExc/PNG/mass_kk.png>
http://hadron.physics.fsu.edu/~mukesh/files/pKKExc/PNG/Dval_vs_masskk.png<http://hadron.physics.fsu.edu/%7Emukesh/files/pKKExc/PNG/Dval_vs_masskk.png>
http://hadron.physics.fsu.edu/~mukesh/files/pKKExc/PNG/D-Func_Profile.png<http://hadron.physics.fsu.edu/%7Emukesh/files/pKKExc/PNG/D-Func_Profile.png>
http://hadron.physics.fsu.edu/~mukesh/files/pKKExc/PNG/Moments_test.png<http://hadron.physics.fsu.edu/%7Emukesh/files/pKKExc/PNG/Moments_test.png>

5. As for the mystery of number of entries, I dumped the H32 histogram information and came across the following.

fEntries                      2625.38     Number of entries
fTsumw                        -2625.38    Total Sum of weights
fTsumw2                       10124.6     Total Sum of squares of weights

Look at :

http://root.cern.ch/root/html/src/TH1.cxx.html#nGY5DE

Conclusion:

The number of entries I showed on each histogram is defined by the root function GetEffectiveEntries() and is generally the "abs(Sum of Weights)". This 'Weight' is equal to the product of the binEntries (h1_binvalue, h2_binvalue) of the 2 histograms and their weights (w1,w2 =1 in this case).

Also the TProfile estimates the correct errors and they are correctly propagated to the Moments I showed earlier.

I will put this justification up on the wiki along with the code and the scripts for calculating the D-Functions and the Moments, if a majority agrees.

Let me know your opinion,
Mukesh.
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