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Fig. 1

image

Probability distribution of actual distances for a measured parallax for objects distributed homogeneously in a finite sphere for values of ϖ, σ, and Dmax as indicated. The blue line represents Eq. (18). The histogram gives the results of a Monte Carlo simulation which retains objects with 0.198 <ϖ′< 0.202. The black and red lines represent modified versions of Eq. (18) according to Faucher-Giguère & Kaspi (2006) and Verbiest et al. (2012), respectively. The intrinsic distribution given by Eqs. (4) and (5) is shown as a dashed line. All curves are normalized to the same area under the curve.

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