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Brian Jackson edited In_the_next_section_we__.tex
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In the next section, we apply Equation \ref{eqn:eqn:convert_from_observed_to_actual_density} to datasets from real surveys, but as an example, consider the simple observed distribution $\rho(\Gamma_{\rm obs}, P_{\rm obs}) = k P_{\rm obs}^{-2}$. Applying Equation \ref{eqn:convert_from_observed_to_actual_density} gives a distribution of actual parameters as follows:
\begin{equation*}
\rho(\Gamma_{\rm act}, P_{\rm act}) =
4 8 k b_{\rm
max}^2 \Gamma_{\rm act}^{-2} \dfrac{P_{\rm min}}{P_{\rm act} - P_{\rm min}} max}^2\ A_{\rm max}\
\kappa^{-1}\ \upsilon^{-1}\ \Gamma_{\rm
act}^{-1} \sqrt{\dfrac{P_{\rm act}^{-11/3} \left( \dfrac{P_{\rm min}}{P_{\rm act} - P_{\rm
min}}} \upsilon^{-1}\ \kappa^{-1} \Gamma_{\rm act}^{-2/3} P_{\rm act} 2 min}} \right)^{3/2} P_{\rm
act}^{-3} act}^{-2}
\end{equation*}