  The QCD evolution equations in Modified Leading Log Approximation for the
factorial moments of the multiplicity distribution in quark and gluon jets are
numerically solved with initial conditions at threshold by fully taking into
account the energy conservation law. After applying Local Parton Hadron Duality
as hadronization prescription, a consistent quantitative description of
available experimental data for factorial cumulants and factorial moments of
arbitrary order and for their ratio both in quark and gluon jets and in
$e^+e^-$ annihilation is achieved.
