Analyses of multiplicity distributions of e^+e^- and e-p collisions by means of modified negative binomial distribution and Laguerre-type distribution: Interrelation of solutions in stochastic processes

A pure birth stochastic process with several initial conditions is considered.We analyze multiplicity distributions of e^+e^- collisions and e-p collisions, usigthe Modified Negative Binomial Distribution (MNBD) and the Laguerre-type distribution. Several multiplicity distributions show the same minimum \chi^2's values in analyses by means of two formulas: In these cases, we find that a parameter N contained in the MNBD becomes to be large. Taking large N limit in the MNBD, we find that the Laguerre-type distribution can be derived from it. Moreover, from the generalized MNBD we can also derive the generalized Glauber-Lachs formula. Finally stochastic properties of QCD and multiparticle dynamics are discussed.