Modified negative binomial description of the multiplicity distributions in lepton - nucleon scattering ”

where θ = n̄Γ(k)Γ(k+1/μ) and H(·) is the Fox generalized hypergeometric function or H-function. For μ = 1 the NBD is recovered. For μ > 1 Pn is not infinitely divisible and the factorial cumulants of the distribution exhibit nontrivial sign-changing oscillations. Eqs. (2)-(3) involve as special and limiting cases the Poisson transform of numerous classical probability densities such as the Chi, Weibull, Maxwell, Pareto and Lognormal to mention but a few. Since the name Generalized NBD is already in use (not rarely to denote different discrete distributions) we shall call the above H-function extension of the Negative Binomial as HNBD for short. E-mail: [email protected]