tokens: that the former can be used as a reliable proxy for the latter. The random theoretical 1-NNS distribution derived for an infinite media (see Appendix B for the full development) is given by: where is the mean intensity of the random process (the average surface density of stars) and is the 1-NNS. We want to compare this theoretical distribution to the 1-NNS histogram obtained from 10 000 random Monte Carlo samplings within the finite and irregularly-shaped window (see Fig. 3 ). Their respective moments are similar (see Table 2 ), with theoretical moments computed from the following expressions: where , , , , and are the mean, median, variance, standard deviation, and skewness factor (see Appendix B for their derivation). The moments from random Monte Carlo samplings were obtained from: where is the ordered sequence of the 1-NNS from the smallest to the highest value, the standard errors of the moments and the standard error of the median are taken respectively from Ahn Fessler (2003) and Kendall Stuart (1977) . Fig. 3 Probability distribution function (PDF) of the 1-NNS distributions observed in Taurus (solid blue histogram: within the limited window , that is, the three main filaments; dashed blue histogram: the entire Taurus region) and predicted for a random distribution (black histogram: for a Monte Carlo sampling within the window ; red curve: unlimited theoretical random 1-NNS distribution, see Eq. ( 3 )). Both random populations are drawn using the same mean surface density . Increasing the mean density by a factor of two leads to a shift towards the left whose amplitude is represented by the green arrow. The Monte Carlo sampling in a finite window and the unlimited theoretical random 1-NNS do not significantly differ. The 1-NNS distributions computed either in the whole Taurus or within do not significantly differ either. However, the Taurus and random 1-NNS distributions are statistically highly inconsistent, with a -value of 10 for the KS test. The spatial distribution in Taurus is clearly far from being random. We thus conclude that finite size and edge window effects do not significantly alter the distribution of 1-NNS from that obtained in an infinite medium at the level of our observational uncertainties. To prove this statement quantitatively, we use a bootstrapping technique, comparing 10 000 realizations of a) a sample of 1-NNS obtained from standard rejection sampling technique using analytical random 1-NNS distribution (Eq. ( 3 )) to b) the 1-NNS associated to random Monte Carlo samplings of 252 stars enclosed within . The two-sample Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) statistical tests indicate that the two 1-NNS distributions cannot be statistically distinguished with a mean -value and standard deviation respectively of for the KS test and for the AD test. We have therefore shown that the random theoretical 1-NNS probability density function (Eq. ( 3 )) may be used as a reliable proxy to describe a 1-NNS
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