Changes between Version 208 and Version 209 of DatabaseBasedAnalysis/Spectrum

Timestamp:

12/09/19 16:19:48 (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. 
 
-Assuming \(\sigma(\Delta T)=0\) gives
-
-\[\sigma^2(\tau_i) = \left[\frac{d\tau_i}{dN_i}\sigma(N_i)\right]^2=\left[\tau_0\frac{\Delta T_i}{N_i^2}\sigma(N_i)\right]^2= \left[\tau_0\frac{\Delta T_i}{N_i^2}\right]^2\cdot N_i\]
+\[\sigma^2(\tau_i) = \left[\frac{d\tau_i}{d\Delta T_i}\sigma(\Delta T_i)\right]^2+\left[\frac{d\tau_i}{dN_i}\sigma(N_i)\right]^2=\left[\tau_0\frac{\Delta T_i}{N_i^2}\sigma(N_i)\right]^2= \left[\tau_0\frac{\Delta T_i}{N_i^2}\right]^2\cdot N_i\]