The negative binomial distribution has become increasingly popular as a more flexible alternative to Poisson distribution, especially when it is questionable whether the strict requirements for Poisson distribution could be satisfied. But negative binomial distribution is better for overdispersed count data that are not necessarily heavy-tailed, for heavy tailed count data the traditional stati...

Let F q X] denote a polynomial ring over a nite eld F q with q elements. Let P n be the set of monic polynomials over F q of degree n. Assuming that each of the q n possible monic polynomials in P n is equally likely, we give a complete characterization of the limiting behavior of P((n = m) as n ! 1 by a uniform asymptotic formula valid for m 1 and n?m ! 1, where n represents the number (multip...

We investigate the KNO scaling function of the modified negative binomial distribution (MNBD), because this MNBD can explain the oscillating behaviors of the cumulant moment observed in e+e− annihilations and in hadronic collisions. By using a straightforward method and the Poisson transform we derive the KNO scaling function from the MNBD. The KNO form of experimental data in e+e− collisions a...