  The phenomenology of velocity statistics in turbulent flows, up to now,
relates to different models dealing with either signed or unsigned longitudinal
velocity increments, with either inertial or dissipative fluctuations. In this
paper, we are concerned with the complete probability density function (PDF) of
signed longitudinal increments at all scales. First, we focus on the symmetric
part of the PDFs, taking into account the observed departure from scale
invariance induced by dissipation effects. The analysis is then extended to the
asymmetric part of the PDFs, with the specific goal to predict the skewness of
the velocity derivatives. It opens the route to the complete description of all
measurable quantities, for any Reynolds number, and various experimental
conditions. This description is based on a single universal parameter function
D(h) and a universal constant R*.
