  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.
