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tokens: for the Galactic bar (Dehnen 2000 ). For all of the following calculations, we assumed a rotation velocity of 220 km s −1 (Kerr Lynden-Bell 1986 ; Bovy et al. 2012 ), a distance to the Galactic centre of 8.2 kpc (Bland-Hawthorn Gerhard 2016 ), and the same peculiar solar motion as in Section 3 , and we integrated forward in time up to 1 Gyr. The galpy software allows one to calculate parameters of individual orbits, including e.g. eccentricity e , maximum height above or below the Galactic plane z max , and peri and apocenter of the orbit, r peri and r apo , respectively. For each star, we ran a Monte Carlo simulation. We calculated 200 orbital solutions in which we varied the initial conditions (proper motions, radial velocities, and distances) within their uncertainties assuming that their distribution is Gaussian. From the resulting distribution, we calculated the median orbital parameters for both Oosterhoff groups. The results are listed in Table 2 . In order to test the differences between the two Oosterhoff groups we used the CM test (see Section 3 ). For the entire distribution of orbital parameters z max , e, r peri , and r apo , the CM test yields p CM = 0.68, there is no statistical evidence that the two distributions are not identical. Table 2. Median values of calculated parameter orbits for the individual Oosterhoff groups. Column 1 lists the studied components, columns 2 and 3 list values for each Oosterhoff group. Fig. 5 depicts the distribution of apocentric distances for the studied RR Lyrae stars. In this diagram, we see that both Oosterhoff groups have very similar apocentric distance distributions. We also noticed a sudden decrease at ≈ 3 kpc (log( r apo ≈ 0.5 kpc), which is roughly in agreement with the overlap between bulge, metal-weak thick disc, and inner halo (3.5 kpc; Ness et al. 2013b ). In fact, the majority of the RR Lyrae stars in our sample stay inside the bulge volume during their full orbits. Figure 5. The distribution of apocentric distances for the studied variables. The blue and red histograms represent the Oo I and Oo II groups, respectively. Based on the negligible difference in the median value of z max between the two Oosterhoff groups, we explored whether the Oo II variables could follow higher orbits from the Galactic plane and thus possibly come from the halo. Based on the distribution of apocentric distances (Fig. 5 ), as a nominal boundary for the Galactic bulge we chose z max > 3 kpc (roughly above ± 20 deg at the distance of the Galactic bulge) and calculated the number of stars that fulfil this condition in at least 50 per cent of the iterations of the Monte Carlo simulation. In total, only 34 RR Lyrae stars fulfil the aforementioned condition. Among these 34 variables, 35 per cent belong to the Oo II population. This is a significant increase in comparison with the overall bulge and halo Oosterhoff population where the fraction of Oo II pulsators is around 25 per cent (Drake et al.