Changes between Version 216 and Version 217 of DatabaseBasedAnalysis/Spectrum

Timestamp:

12/09/19 16:40:53 (5 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. 
 
-\[\sigma^2(\tau_i) = \left[\frac{d\tau_i}{d\Delta T_i}\sigma(\Delta T_i)\right]^2+\left[\frac{d\tau_i}{dN_i}\sigma(N_i)\right]^2=\left[\frac{\tau_0}{N_i}\sigma(\Delta T_i)\right]^2+\left[\frac{\tau_0\cdot\Delta T_i}{N_i^2}\sigma(N_i)\right]^2\]
-
-\[\rightarrow\quad\sigma^2(\tau_i) = \tau_i^2\left[\left(\frac{\sigma(\Delta T_i)}{\Delta T_i}\right)^2+\left(\frac{\sigma(N_i)}{N_i}\right)^2\right]\]
+\[\sigma^2(\tau_i) = \left[\frac{d\tau_i}{d\Delta T_i}\sigma(\Delta T_i)\right]^2+\left[\frac{d\tau_i}{dN_i}\sigma(N_i)\right]^2= \tau_i^2\left[\left(\frac{\sigma(\Delta T_i)}{\Delta T_i}\right)^2+\left(\frac{\sigma(N_i)}{N_i}\right)^2\right]\]
 
 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.