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Brian Jackson edited Ultimately_though_we_re_interested__.tex
almost 9 years ago
Commit id: 1f4747d7dd2f1481be981dd6f7a89e74ccc61bee
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Ultimately, though, we're interested in working from the observed distribution back to the underlying distribution. Fortunately, the combined recovery bias and distortion expression provides a simple way to do this:
\begin{equation}\label{eqn:n-Pact_from_n-Pobs}
n(P_{\rm act}) =
-\left( -P_{\rm act}^{-1}\ \left( \dfrac{P_{\rm max} - P_{\rm min}}{P_{\rm
min}\ P_{\rm act}} min}\} \right)\ \left( \frac{d}{dP_{\rm obs}} \right)_{P_{\rm obs} = P_{\rm act}} \bigg[ n(P_{\rm obs})\ P_{\rm obs}^2 \bigg].
\end{equation}