# Changes between Version 20 and Version 21 of DatabaseBasedAnalysis/Spectrum

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Timestamp:
Dec 3, 2019, 5:19:37 PM (10 months ago)
Comment:

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Unmodified
 v20 $\phi(E) = \frac{1}{A_0\cdot \Delta T}\frac{N(\Delta E)}{\epsilon(\Delta E)\cdot \Delta E}$ For simplicity, in the following, $$\Delta E$$ will be replaced by just $$E$$ but always refers to an average quantity in an given energy interval. Note that strictly speaking the average quantity is not independent of the event distribution in that interval so that the calculation are only exact if the correct distribution is assumed! For simplicity, in the following, $$\Delta E$$ will be replaced by just $$E$$ but always refers to to a given energy interval. 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 where $$N_0$$ is the number of simulated events in this energy bin and $$N=N_{exc}$$ the number of *excess* events that are produced by the analysis chain. Note that the exact calculation of the efficiency $$\epsilon(\Delta E)$$ depends on prior knowledge of the correct source spectrum $$N_0$$. 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 $$N_0$$. The number of excess events, for data and simulations, is defined as