Changes between Version 248 and Version 249 of DatabaseBasedAnalysis/Spectrum

Timestamp:

12/10/19 14:22:37 (5 years ago)

Author:

tbretz

Comment:

--

DatabaseBasedAnalysis/Spectrum

@@ -4 +4 @@
 
 == Theory ==
+
+=== Spectrum ===
 
 The differential flux \(\phi(E)\) per area, time and energy interval is defined as
@@ -15 +17 @@
 For simplicity, in the following, \(\Delta E\) will be replaced by just \(E\) but always refers to to a given energy interval. If data is binned in a histogram, the relation between the x-value for the bin \(E_\textrm{x}\) and the corresponding interval \(\Delta E_\textrm{x}\) is not well defined. Resonable definitions are the bin center (usually in logarithmic bins) or the average energy.
 
+=== Efficiency and eff. Collection Area ===
+
 The total area \(A_0\) and the corresponding efficiency \(\epsilon(E)\) are of course only available for simulated data. For simulated data, \(A_0\) is the production area and \(\epsilon(E)\) the corresponding energy dependent efficiency of the analysis chain. For a given energy bin, the efficiency is then defined as 
 
@@ -23 +27 @@
 Note that the exact calculation of the efficiency \(\epsilon(\Delta E)\) depends on prior knowledge of the correct source spectrum \(N_0(E)\). Therefore, it is strictly speaking only correct if the simulated spectrum and the real spectrum are identical. As the real spectrum is unknown, special care has to be taken of the systematic introduced by the assumption of \(N_0(E)\).
 
-=== Excess ===
+=== Excess and Error ===
 
 The number of excess events, for data and simulations, is defined as
@@ -45 +49 @@
 with the Poisson (counting) error \(\sigma^2(N_\textrm{sig,bg}) = N_\textrm{sig,bg}\).
 
-=== Code ===
+=== Weights and Error ===
 
 In the following \(N\) refers to a number of simulated events and \(M\) to a number of measured (excess) events.