Very weird +2sigma band

Dear experts.

In a search, we have very low backgound yield (0.68) and 0.28 signals. We use FrequentistCalculator to get the p-value scanning curves. For each point we use about 10000 toys.
The issue is the +2sigma band seems never converge, no matter how we change the PoI scanning ranges. The other curves (expected, ±1sigma, -2sigma) look quite OK.
please see the attached 4 plots, they are with scanning range 0-20 and 0-4000 respectively. Please kindly help.

Thanks a lot!
HypoTestInverter_Scan_toy10000-Range0To4000.pdf (18.2 KB)
HypoTestInverter_Scan_toy10000-Range0To20.pdf (21.4 KB)
Test_Statistic_Distributions_toy10000-Range0To20.pdf (138 KB)
Test_Statistic_Distributions_toy10000-Range0To4000.pdf (132 KB)


The problem could be caused by some failing fits. It is difficult to see from the attached test statistic plots, but the fact that the 2-sigma band does not converge means that you have a long tail of the test statistic distribution. Is this correct ? Could you make a plot for the test statistic distributions (in log-scale) to see this better ?
If this is correct you should investigate better (using for example the detailed output information) what causes this large tail in the S+B test statistic distribution.

Best Regards


Dear Lorenzo

Thanks a lot for the suggestions! We checked the fittings carefully, wouldn’t see any failed/strange things.
Would you look the attached new test-statistic distribution plots again, we wouldn’t see there are large tails in the S+B test-statistics … maybe I mis-understand what you mean ?
I also copy the workspace to be here:

could you help to investigate a bit ?

Thanks a lot!
Test_Statistic_Distributions_toy10000-Range0To20.v2.pdf (159 KB)

Dear all

could anyone help on this? We tried many ideas but the problem is still not solved …

Thanks & Regards,