Changes between Version 15 and Version 16 of DatabaseBasedAnalysis/Spectrum

Timestamp:

12/03/19 17:07:02 (5 years ago)

Author:

tbretz

Comment:

--

DatabaseBasedAnalysis/Spectrum

@@ -17 +17 @@
 The number of excess events, for data and simulations, is defined as
 
-\[N_\textrm{exc} = N_\textrm{sig} - N_\textrm{bg}\]
+\[N_\textrm{exc} = N_\textrm{sig} - \hat N_\textrm{bg}\]
 
-where \(N_\textrm{sig}\) is the number of events identified as potential gammas from the source direction ('on-source') and \(N_\textrm{bg}\) the number of gamma-like events measured 'off-source'. Note that for Simulations, \(N_\textrm{bg}\) is not necessarily zero for wobble-mode observations as an event can survive the analysis for on- and off-events, if this is not protected by the analysis chain.
+where \(N_\textrm{sig}\) is the number of events identified as potential gammas from the source direction ('on-source') and \(N_\textrm{bg}\) the number of gamma-like events measured 'off-source'. Note that for Simulations, \(\hat N_\textrm{bg}\) is not necessarily zero for wobble-mode observations as an event can survive the analysis for on- and off-events, if this is not protected by the analysis chain.
+
+The average number of background events \(\hat N_\textrm{bg}\) is the total number of background events \(\N_\textrm{bg}\) from all off-regions times the corresponding weight \(\omega\). For five off-regions, this yields
+
+\[\(\hat N_\textrm{bg}\) = \frac{N_\textrm{bg}}{5}\]