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Stellar distribution functions in the solar neighbourhood using star samples such as the Hipparcos database

The Hipparcos catalogue provides a large amount of high quality positional and kinematical data of stars in the solar neighbourhood. In principle, these data can be used to construct a distribution function for the orbits of the stars, assuming three integrals of the motion and an axisymmetric potential of Stackel type. Since orbits are not local, the construction of a distribution function is the better conditioned the larger the volume covered by the data. 
On galactic scales however, the Hipparcos data cover a fairly restricted volume. To assess to what extent the distribution function derived from these data will be useful to determine a (unknown) distribution function, we generated Hipparcos-like artificial data samples coming from a known (global) distribution function, and investigate how well this distribution function can be recovered. The distribution function is constructed by fitting an analytical, but flexible form of the distribution function to the data.