  We report experimental results on the acceleration component probability
distribution function at $R_\lambda = 690$ to probabilities of less than
$10^{-7}$. This is an improvement of more than an order of magnitude over past
measurements and allows us to conclude that the fourth moment converges and the
flatness is approximately 55. We compare our probability distribution to those
predicted by several models inspired by non-extensive statistical mechanics. We
also look at acceleration component probability distributions conditioned on a
velocity component for conditioning velocities as high as 3 times the standard
deviation and find them to be highly non-Gaussian.
