Distribution of the orbital energy E vs. the z-component of the angular momentum L_z (top panel). The bottom panel shows an example of the multivariate non-normal distribution of energies E vs. angular momenta for one of the stars from our sample (represented with blue squares) and Grus II (denoted with red circles). The underlying gray points in the upper panel represent the entire RR Lyrae sample fulfilling the condition in Eq. (1). The blue squares represent the RR Lyrae variables associated with the Orphan stellar stream. Each point is accompanied with an error ellipse estimated based on our Monte Carlo simulation. The position of Grus II is marked with the red dot and dashed lines accompanied by error ellipses representing the covariances.