The maximum entropy approach is proposed to describe the local structures of the veloc-
ity distribution, which are collected through its sample moments. The method is used with
several samples from the HIPPARCOS and Geneva-Copenhagen survey catalogues. For the
large-scale distribution, the phase density function may be obtained by fitting moments up
to sixth order as a product of two exponential functions, one giving a background ellipsoidal
shape of the distribution and the other accounting for the skewness and for the slight shift in
the ellipsoidal isocontours in terms of the rotation velocity. The small-scale distribution can
be deduced from truncated distributions, such as velocity-bounded samples with |V| ≤ 51
km s−1, which contain a complex mixture of early-type and young disc stars. By fitting up
to ten-order moments, the maximum entropy approach gives a realistic portrait of actual
asymmetries, showing a clear bimodal pattern: (i) around the Hyades-Pleiades stream, with
negative radial mean velocity and (ii) around the Sirius-UMa stream, with slightly positive
radial mean velocity. The “U-anomaly” along the radial direction is estimated straightfor-
wardly 30 − 35 km s−1 from the contour plots.Preprin
