  Analysis of 15314 electron velocity distribution functions (VDFs) within
$\pm$2 hours of 52 interplanetary (IP) shocks observed by the \emph{Wind}
spacecraft near 1 AU are introduced. The electron VDFs are fit to the sum of
three model functions for the cold dense core, hot tenuous halo, and
field-aligned beam/strahl component. The best results were found by modeling
the core as either a bi-kappa or a symmetric (or asymmetric) bi-self-similar
velocity distribution function, while both the halo and beam/strahl components
were best fit to bi-kappa velocity distribution function. This is the first
statistical study to show that the core electron distribution is better fit to
a self-similar velocity distribution function than a bi-Maxwellian under all
conditions. The self-similar distribution deviation from a Maxwellian is a
measure of inelasticity in particle scattering from waves and/or turbulence.
The range of values defined by the lower and upper quartiles for the kappa
exponents are $\kappa{\scriptstyle_{ec}}$ $\sim$ 5.40--10.2 for the core,
$\kappa{\scriptstyle_{eh}}$ $\sim$ 3.58--5.34 for the halo, and
$\kappa{\scriptstyle_{eb}}$ $\sim$ 3.40--5.16 for the beam/strahl. The
lower-to-upper quartile range of symmetric bi-self-similar core exponents are
$s{\scriptstyle_{ec}}$ $\sim$ 2.00--2.04, and asymmetric bi-self-similar core
exponents are $p{\scriptstyle_{ec}}$ $\sim$ 2.20--4.00 for the parallel
exponent, and $q{\scriptstyle_{ec}}$ $\sim$ 2.00--2.46 for the perpendicular
exponent. The nuanced details of the fit procedure and description of resulting
data product are also presented. The statistics and detailed analysis of the
results are presented in Paper II and Paper III of this three-part study.
