Changes between Version 210 and Version 211 of DatabaseBasedAnalysis/Spectrum

Timestamp:

12/09/19 16:25:56 (6 years ago)

Author:

tbretz

Comment:

--

DatabaseBasedAnalysis/Spectrum

@@ -118 +118 @@
 where \(N(\delta\theta)\) is the number of produced events in the interval \(\delta\theta\) and \(\Delta T(\delta\theta)\) is the total observation time in the same zenith angle interval. \(\tau_0\) is the normalization constant. 
 
-\[\sigma^2(\tau_i) = \left[\frac{d\tau_i}{d\Delta T_i}\sigma(\Delta T_i)\right]^2+\left[\frac{d\tau_i}{dN_i}\sigma(N_i)\right]^2=\left[\frac{\tau_0}{N_i}\sigma(\Delta T_i)\right]^2+\left[\frac{\tau_0\cdot\Delta T_i}{N_i^2}\sigma(N_i)\right]^2= \left[\frac{\tau_0\cdot\Delta T_i}{N_i^2}\right]^2\cdot N_i\]
-
+\[\sigma^2(\tau_i) = \left[\frac{d\tau_i}{d\Delta T_i}\sigma(\Delta T_i)\right]^2+\left[\frac{d\tau_i}{dN_i}\sigma(N_i)\right]^2=\left[\frac{\tau_0}{N_i}\sigma(\Delta T_i)\right]^2+\left[\frac{\tau_0\cdot\Delta T_i}{N_i^2}\sigma(N_i)\right]^2\]
+
+While \(\sigma(\Delta T_i)\) is given by the data acquisition and 1s per run, \(sigma^2(N_i)=N_i\) is just the statistical error \(\sqrt{N_i}\) of the number of events event counting.
 
 As the efficiency \(\epsilon(\delta E)\) for an energy interval \(\delta E\) is calculated as
@@ -130 +131 @@
 
 \[\phi(\delta E) = \phi(\delta E,\Delta\Theta) = \frac{1}{A_0\cdot \Delta T}\frac{M_\textrm{exc}(\delta E)}{\epsilon(\delta E)\cdot \delta E} = \frac{M_\textrm{exc}(\delta E)}{N'_\textrm{exc}(\delta E)}\cdot \frac{N'_\textrm{src}(\delta E)}{A_0\cdot\Delta T\cdot \delta E}\]
+