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Antonino Ingargiola edited Burst_Weights_Theory.tex
about 8 years ago
Commit id: dba9b0b6bfbbeae059e8e8fc969dc4e17bf606e4
deletions | additions
diff --git a/Burst_Weights_Theory.tex b/Burst_Weights_Theory.tex
index b3f09ea..3cd0552 100644
--- a/Burst_Weights_Theory.tex
+++ b/Burst_Weights_Theory.tex
...
\hat{E} = \frac{\sum_i n_{ai}}{\sum_i n_{ti}}
\end{equation}
The variance of $\hat{E}$
(eq.~\ref{eq:E_var}) (eq.~\ref{eq:E_variance}) is equal to the inverse of
the Fisher information $\mathcal{I}(\hat{E})$ and therefore $\hat{E}$ is a MVUB
estimator for $E_p$.
\begin{equation}
\label{eq:E_var}
\operatorname{Var}(\hat{E}) = \frac{E_p (1 - E_p)}{\sum_i n_{ti}} \label{eq:E_variance}
\frac{1}{\mathcal{I}(\hat{E})}
\end{equation}
With simple algebra is verify that $\hat{E}$ is equal to the weighted average of the bursts