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tokens: region. The distribution under the hypothesis that HMXBs are displaced from their parent star-forming region (the grey histogram) is extended compared with the distribution under the null hypothesis (the yellow histogram). We next quantify the observed displacement of HMXBs, which is attributed to kicks after an asymmetric SN explosion during the formation of the compact object (Fryer Kalogera 1997 ). The contribution of natal kicks is treated as a Gaussian smearing function of standard deviation σ that broadens the spatial distribution of HMXBs compared with their birth distribution. We simulate the vertical distribution of HMXBs from the mid-plane as the convolution P ( z |σ, z sfr ) between this Gaussian and the exponential distribution of SFR (equation 2 ) with a scale height of z sfr = 330 pc .: We apply the maximum likelihood method for finding the best estimate of the Gaussian smearing parameter σ. The likelihood function L ( z |σ, z sfr ) derived from the convolution P is where N = 41 is the number of HMXBs and z i is the vertical distance of the i th HMXB from the mid-plane of NGC 55. We perform 100 000 iterations and in order to account for the estimated AGN contamination, in each iteration our HMXB sample consists of all ‘verified HMXBs’ (Table 3 ) as well as randomly selected combinations of 22 out of 37 ‘candidate HMXBs’ (Table 3 ). In Fig. 10 we show the likelihood of the dispersion of the Gaussian smearing function (normalized to the maximum likelihood). The maximum at σ = 0.57 ± 0.07 kpc is the difference between the scale height of the vertical distribution of HMXBs and the vertical distribution of star-forming activity. In Fig. 11 we show the simulated vertical distribution of HMXBs (black dashed line) as the convolution between a Gaussian smearing function of standard deviation σ = 0.57 kpc (green line) that represents the contribution of natal kicks, on top of their birth distribution of 0.33 kpc (red line). Figure 10. The likelihood of the dispersion of the Gaussian smearing function (normalized to the maximum likelihood σ), described in Section 3.2 . The maximum at σ = 0.57 kpc is the scale height corresponding to the displacement between HMXBs and star-forming regions. Figure 11. Simulated vertical distribution of HMXBs (black dashed) as the convolution between a Gaussian smearing function of standard deviation σ = 0.57 kpc (green) that represents the contribution of kicks, on top of the their birth distribution of 0.33 kpc (red). The grey and yellow histograms show the observed vertical distribution of candidate and verified HMXBs, respectively. 3.3 Constraining the displacement of HMXBs The result of the previous section mainly provides an upper limit on the scale height of HMXBs. There are other factors such as contamination, incompleteness and in situ formation of HMXBs that would bias the result of this analysis toward larger scale heights. We investigate these factors in an effort to constrain the lower limit on