Investigation of the errors in SDSS proper-motion measurements using
  samples of quasars
  We investigate in detail the probability distribution function (pdf) of the
proper-motion measurement errors in the SDSS+USNO-B proper-motion catalog of
\citet{mun04} using clean quasar samples. The pdf of the errors is
well-represented by a Gaussian core with extended wings, plus a very small
fraction ($<0.1%$) of "outliers". We find while formally the pdf could be
well-fit by a five-parameter fitting function, for many purposes it is also
adequately to represent the pdf with a one-parameter approximation to this
function. We apply this pdf to the calculation of the confidence intervals on
the true proper motion for a SDSS+USNO-B proper motion measurement, and discuss
several scientific applications of the SDSS proper motion catalogue. Our
results have various applications in studies of the galactic structure and
stellar kinematics. Specifically, they are crucial for searching hyper-velocity
stars in the Galaxy.
