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<div style="direction: ltr;font-family: Tahoma;color: #000000;font-size: 10pt;">Hello All,<br>
<br>
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.<br>
<br>
I am better able to explain if you follow the process of the way I calculate the moments and the associated errors.
<br>
<br>
1. I calculate the Big-D function value for each event for different J,M,N and save those in an ntuple.<br>
<br>
2. I histogram in 2D the D-Function vs Mass_kk<br>
<br>
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:<br>
<br>
http://root.cern.ch/root/html/TProfile.html<br>
<pre>"Profile histograms are used to display the mean
value of Y and its error for each bin in X. <br>The displayed error is by default the
standard error on the mean (i.e. the <br>standard deviation divided by the sqrt(n) )"</pre>
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.<br>
<br>
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.
<br>
<br>
Relevant Plots to check:<br>
<br>
<a href="http://hadron.physics.fsu.edu/%7Emukesh/files/pKKExc/PNG/mass_kk.png" target="_blank">http://hadron.physics.fsu.edu/~mukesh/files/pKKExc/PNG/mass_kk.png</a><br>
<a href="http://hadron.physics.fsu.edu/%7Emukesh/files/pKKExc/PNG/Dval_vs_masskk.png" target="_blank">http://hadron.physics.fsu.edu/~mukesh/files/pKKExc/PNG/Dval_vs_masskk.png</a><br>
<a href="http://hadron.physics.fsu.edu/%7Emukesh/files/pKKExc/PNG/D-Func_Profile.png" target="_blank">http://hadron.physics.fsu.edu/~mukesh/files/pKKExc/PNG/D-Func_Profile.png</a><br>
<a href="http://hadron.physics.fsu.edu/%7Emukesh/files/pKKExc/PNG/Moments_test.png" target="_blank">http://hadron.physics.fsu.edu/~mukesh/files/pKKExc/PNG/Moments_test.png</a><br>
<br>
5. As for the mystery of number of entries, I dumped the H32 histogram information and came across the following.<br>
<br>
fEntries 2625.38 Number of entries<br>
fTsumw -2625.38 Total Sum of weights<br>
fTsumw2 10124.6 Total Sum of squares of weights<br>
<br>
Look at :<br>
<br>
http://root.cern.ch/root/html/src/TH1.cxx.html#nGY5DE<br>
<br>
<u>Conclusion: </u><br>
<br>
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). <br>
<br>
Also the TProfile estimates the correct errors and they are correctly propagated to the Moments I showed earlier.<br>
<br>
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.<br>
<br>
Let me know your opinion,<br>
Mukesh.</div>
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