H-function extension of the NBD in the light of experimental data

Abstract

The recently introduced H-function extension of the Negative Binomial Distribution is investigated. The analytic form of P(n) is rederived by means of the Mellin transform. Applications of the HNBD are provided using experimental data for P(n) in e+e-, e+p, inelastic pp and non-diffractive p-pbar reactions.Comment: 8 pages REVTeX, 1 eps figure embedde

H-function extension of the NBD: further applications

“…(15) and (17) for the analytic form of P n and G(u). Our result completes the specification of the Poisson transformed generalized gamma distribution introduced in [1] and developed in [2,3]. Its application to multihadron and galaxy count data revealed µ < 0 type behaviour in both cases.…”

“…The effect is illustrated in Fig. 1 for shape parameter k = 1 (Weibull case) which describes the inelastic pp and deep-inelatic e + p multipilicity data very well [2,3]. Bondesson's theorem tells us that sign-changing oscillations of the factorial cumulants may arise also for µ < −1.…”

“…The analytic form of P n was shown to be expressible in terms of Fox's H-function (see refs. [1,3] for a summary and ref. [6] for details).…”

“…It corresponds to the NBD fitted in two matched domains of multiplicity n with 3 fit parameters altogether. The HNBD analysis was carried out with fixed shape parameter k = 1 (details of the fitting procedure can be found in [1,3]). This particular case of the HNBD produces This change in the parametrization of the best-fit HNBD indicates a slight narrowing of the KNO functions with increasing s in the energy range investigated.…”

“…In ref. [3] it was shown that long tailed distributions such as the P n in pp collisions at √ s = 900 GeV can be successfully described by the µ → 0, k → ∞ limit of the HNBD. Fitting the Poisson transformed log-normal law to our galaxy data one obtains further improvement, see the bottom left plot in Fig.…”