ANALYSES OF MULTIPLICITY DISTRIBUTIONS BY MEANS OF THE MODIFIED NEGATIVE BINOMIAL-DISTRIBUTION AND ITS KNO SCALING FUNCTION

We analyze various data of multiplicity distributions by means of the modified negative binomial distribution (MNBD) and its KNO scaling fun ction; since the MNBD explains the oscillating behavior of the cumulan t moment observed in e(+)e(-) annihilations, h-h collisions and e-p co llisions. In the present analyses, we find that the MNBD (discrete dis tribution) describes the data of charged particles in e(+)e(-) annihil ations much better than the negative binomial distribution (NBD). To i nvestigate stochastic properties of the MNBD, we derive the KNO scalin g function from the discrete distribution by using a straightforward m ethod and the Poisson transform. This 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 stated that the MNBD is a useful formula, as is the NBD.