We analyze various data of multiplicity distributions by means of the
Modified Negative Binomial Distribution (MNBD) and its KNO scaling function,
since this MNBD explains the oscillating behavior of the cumulant moment
observed in e^+e^- annihilations, h-h collisions and e-p collisions. In the
present analyses, we find that the MNBD(discrete distributions) describes the
data of charged particles in e^+e^- annihilations much better than the Negative
Binomial Distribution (NBD). To investigate stochastic property of the MNBD, we
derive the KNO scaling function from the discrete distribution by using a
straightforward method and the Poisson transform. It is a new KNO function
expressed by the Laguerre polynomials. In analyses of the data by using the KNO
scaling function, we find that the MNBD describes the data better than the
gamma function.Thus, it can be said that the MNBD is one of useful formulas as
well as NBD.Comment: 12 pages, latex, 3 figure