Changes between Version 213 and Version 214 of DatabaseBasedAnalysis/Spectrum


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Timestamp:
12/09/19 16:32:15 (5 years ago)
Author:
tbretz
Comment:

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  • DatabaseBasedAnalysis/Spectrum

    v213 v214  
    120120\[\sigma^2(\tau_i) = \left[\frac{d\tau_i}{d\Delta T_i}\sigma(\Delta T_i)\right]^2+\left[\frac{d\tau_i}{dN_i}\sigma(N_i)\right]^2=\left[\frac{\tau_0}{N_i}\sigma(\Delta T_i)\right]^2+\left[\frac{\tau_0\cdot\Delta T_i}{N_i^2}\sigma(N_i)\right]^2\]
    121121
    122 \[\rightarrow\quad\sigma^2(\tau_i) = \left(\frac{\tau_0}{N_i}\right)^2\cdot\left(\sigma^2(\Delta T_i)+\frac{\Delta T_i^2}{N_i}\right)\]
     122\[\rightarrow\quad\sigma^2(\tau_i) = \left(\frac{\tau_0}{N_i}\right)^2\cdot\left[\sigma^2(\Delta T_i)+\frac{\Delta T_i^2}{N_i}\right]\]
    123123
    124124While \(\sigma(\Delta T_i)\) is given by the data acquisition and 1s per run, \(\sigma^2(N_i)=N_i\) is just the statistical error \(\sqrt{N_i}\) of the number of events event counting.