Line 102: |
Line 102: |
| | | |
| <math> | | <math> |
− | \sum_{p,s} e^-(\lambda_p) \lambda_p^p | + | f(q) = \sum_{p,s} \left(\frac{e^{-\lambda_{(p)}} \lambda_{(p)}^p}{p!}\right)\left(\frac{e^{-p \lambda_{(s)}}(p \lambda_{(s)})^s}{s!}\right) \left(\frac{\exp \left(-\frac{1}{2}\; \frac{\left[q-(p+s)\right]^2}{\sigma_0^2+(p+s)\sigma_1^2}\right) } {\sqrt{2\pi}\left[\sigma_0^2+(p+s)\sigma_1^2\right]^{\frac{1}{2}} }\right) |
| </math> | | </math> |
| + | |
| + | where, |
| + | {| border="0" cellpadding="0" |
| + | |- |
| + | |<math>q \equiv \frac{x-x_0}{g}\quad</math> ||width="50px"| || a unit normalized to pixel counts (and zeroed accordingly) |
| + | |- |
| + | |<math>x\quad</math> || || is the real integral value (in Vs) and <math>x_0</math> is the pedestal offset (location of first peak). |
| + | |- |
| + | |<math>p, \lambda_{(p)}\quad</math> || || is the pixel count and Poisson average pixel count |
| + | |- |
| + | |<math>s, \lambda_{(s)}\quad</math> || ||are multi-Poisson factors that take into account Poisson distributions of secondary pixel counts per each real hit from the set of p hits. |
| + | |- |
| + | |<math>\sigma_0, \sigma_1\quad</math> || || are random noise parameters. |
| + | |- |
| + | |} |
| | | |
| ==== rest ==== | | ==== rest ==== |