Changes between Version 203 and Version 204 of DatabaseBasedAnalysis/Spectrum

Timestamp:

12/09/19 16:00:01 (5 years ago)

Author:

tbretz

Comment:

--

DatabaseBasedAnalysis/Spectrum

@@ -197 +197 @@
 == Errors ==
 
-For a sum of weights, e.g. \(R = \sum_N \rho_i\tau_i\) the corresponding error is
-\[\sigma_R^2 = \sum_N\left[\rho_i\cdot\sigma(\tau_i)+\tau_i\cdot\sigma(\rho_i)\right]^2\] 
+For a sum of weights, e.g. \(N' = \sum_N \rho_i\tau_i\) the corresponding error is
+\[\sigma^2(N')^2 = \sum_N\left[\rho_i\cdot\sigma(\tau_i)+\tau_i\cdot\sigma(\rho_i)\right]^2\] 
+
+As the energy is well defined, \(\sigma(\rho_i)=0\) and thus
+
+\[\sigma^2(N')^2 = \sum_N\rho_i^2\cdot\sigma^2(\tau_i)\]