Changes between Version 205 and Version 206 of DatabaseBasedAnalysis/Spectrum

Timestamp:

12/09/19 16:12:56 (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. 
 
+Assuming \(\sigma(\Delta T)=0\) gives
+
+\[\sigma^2(\tau_i) = \left[\tau_0\frac{\Delta T_i^2}{N_i^2}\sigma(N_i)\right]^2= \left[\tau_0\frac{\Delta T_i^2}{N_i^2}\right]^2\cdot N_i\]
+
+
 As the efficiency \(\epsilon(\delta E)\) for an energy interval \(\delta E\) is calculated as
 
@@ -149 +154 @@
 \[= \left(\frac{1}{A_0\cdot \Delta T\cdot\delta E\cdot N'_\textrm{exc}}\right)^2\cdot\left[\left(N'_\textrm{src}\right)^2\sigma^2(M_\textrm{exc}) + \left(\phi'\right)^2\sigma^2(N'_\textrm{exc}) + \left(M_\textrm{exc}\right)^2\sigma^2(N'_\textrm{src})\right]\]
 
-
-
-
-\[\sigma^2(N') = \sum_m\left(\frac{dN'}{d\rho_m}\sigma(\rho_m)\right)^2+\sum_n\left(\frac{dN'}{d\tau_n}\sigma(\tau_n)\right)^2\]
-
-\[=\sum_m\left(\sum_j\tau(\theta_j)\sigma(\rho_m)\right)^2+\sum_n\left(\sum_i\rho(E_i)\sigma(\theta_n)\right)^2\]
-
-\[=\sum_m\sigma^2(\rho_m)\left(\sum_j\tau(\theta_j)\right)^2+\sum_n\sigma^2(\theta_n)\left(\sum_i\rho(E_i)\right)^2\]
-
-\[\sigma^2(\rho_m) = 0\]
-
-\[\sigma^2(\theta_n) = \frac{\tau_0^2\Delta T_n^2}{N_n^4}\sigma^2(N_n)= \frac{\tau_0^2\Delta T_n^2}{N_n^3}\]
-
-\[\sigma^2(N') = \tau_0^2\left(\sum_{n\in\Delta\Theta}\frac{\Delta T_n^2}{N_n^3}\right)\left(\sum_{i\in\delta E}\rho(E_i)\right)^2\]
-
 === Monte Carlo ===