Changes between Version 209 and Version 210 of DatabaseBasedAnalysis/Spectrum


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Timestamp:
12/09/19 16:21:57 (5 years ago)
Author:
tbretz
Comment:

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  • DatabaseBasedAnalysis/Spectrum

    v209 v210  
    118118where \(N(\delta\theta)\) 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.
    119119
    120 \[\sigma^2(\tau_i) = \left[\frac{d\tau_i}{d\Delta T_i}\sigma(\Delta T_i)\right]^2+\left[\frac{d\tau_i}{dN_i}\sigma(N_i)\right]^2=\left[\tau_0\frac{\Delta T_i}{N_i^2}\sigma(N_i)\right]^2= \left[\tau_0\frac{\Delta T_i}{N_i^2}\right]^2\cdot N_i\]
     120\[\sigma^2(\tau_i) = \left[\frac{d\tau_i}{d\Delta T_i}\sigma(\Delta T_i)\right]^2+\left[\frac{d\tau_i}{dN_i}\sigma(N_i)\right]^2=\left[\frac{\tau_0}{N_i}\sigma(\Delta T_i)\right]^2+\left[\frac{\tau_0\cdot\Delta T_i}{N_i^2}\sigma(N_i)\right]^2= \left[\frac{\tau_0\cdot\Delta T_i}{N_i^2}\right]^2\cdot N_i\]
    121121
    122122