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\subsection{Converting Between the Observed and Actual Parameter Distributions}  Consider a distribution of observed values $\rho(\Gamma_{\rm obs}, P_{\rm obs}) = \dfrac{d^2N}{d\Gamma_{\rm obs}\ dP_{\rm obs}}$. The small number of devils $dN = f\ \rho(\Gamma_{\rm obs}, P_{\rm obs})\ d\Gamma_{\rm act}\ dP_{\rm act}$ contributing are those that had closest approach distances between $b$ and $b + db$ of the detector. Thus, we can convert $\rho(\Gamma_{\rm act}, P_{\rm act})$ to $\rho(\Gamma_{\rm obs}, P_{\rm obs})$ by integrating the former density over $b$ and accounting for the bias and distortion effects. To calculate the integral, we also need to re-cast the upper limit to express the maximum possible radial distance, i.e. the distance at which $P_{\rm act} = P_{\rm max}$. Using Equation \ref{eqn:b} and making the replacements $P_{\rm act} = P_{\rm max}$ and $\Gamma_{\rm act} = \left( P_{\rm obs}/P_{\rm max} \right)^{1/2} \Gamma_{\rm obs}$ from Equation \ref{eqn:P_obs_Gamma_obs} gives $b(\Gamma_{\rm obs}, P_{\rm obs}) = \left(\Gamma_{\rm obs}/2\right) \left[ \left(P_{\rm max} - P_{\rm obs}\right)/P_{\rm max} \right]^{1/2}$. The integral to convert from $\rho({\rm act}) \equiv \rho(P_{\rm act}, \Gamma_{\rm act})$ to $\rho({\rm obs}) \equiv \rho(\Gamma_{\rm obs}, P_{\rm obs})$ is then   \begin{align} \begin{eqnarray}  \rho({\rm obs}) & = & & \int_{b^\prime = 0}^{b({\rm obs})} f\ \rho({\rm act}(b^\prime))\ \dfrac{2b^\prime\ db^\prime}{b_{\rm max}^2} & \\  & =& & 2\ A_{\rm max}^{-1}\ \upsilon\ \kappa\ b_{\rm max}^{-2} P_{\rm min}^{-1/2}\ \int_{b^\prime = 0}^{b({\rm obs})} \left( \Gamma_{\rm act}(b^\prime)/{\rm m} \right)^{5/3} \left( P_{\rm act}(b^\prime) - P_{\rm min} \right)^{1/2} \ \rho({\rm act}(b^\prime))\ b^\prime\ db^\prime \label{eqn:convert_from_actual_to_observed_density} & ,   \end{align} \end{eqnarray}  where $\kappa = 40\ {\rm s}$ and $\Gamma_{\rm act}$ is measured in meters, m. Figure \ref{fig:uniform_actual_distribution_to_observed_distribution} shows the result for a uniform distribution of actual values, $\rho({\rm act}) = \left( P_{\rm max} - P_{\rm min} \right)^{-1}\ \left( \Gamma_{\rm max} - \Gamma_{\rm min} \right)^{-1}$ and compares it to a simulated dust devil survey (blue circles). (For the uniform distribution, the integral has a closed form expression that is unwieldy, so we opt to perform the integration numerically.)