Multiplicity distributions in strong interactions: a generalized negative binomial model

Multiplicity Distributions in Strong Interactions: a Generalized Negative Binomial Model

A three-parameter discrete distribution is developed to describe the multiplicity distributions observed in totaland limited phase space volumes in different collision processes. The probability law is obtained by the Poisson transform of the KNO scaling function derived in Polyakov’s similarity hypothesis for strong interactions as well as in perturbative QCD, ψ(z) ∝ zα exp(−zμ). Various chara...

GENERALIZED BINOMIAL AND NEGATIVE BINOMIAL DISTRIBUTIONS OF ORDER k BY THE/-OVERLAPPING ENUMERATION SCHEME

A b s t r a c t . In this paper, we investigate the exact distribution of the waiting time for the r-th t-overlapping occurrence of success-runs of a specified length in a sequence of two state Markov dependent trials. The probability generating functions are derived explicitly, and as asymptotic results, relationships of a negative binomial distribution of order k and an extended Poisson distr...

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, ...

On Hypergeometric Generalized Negative Binomial Distribution

The Negative Binomial Distribution Efficiency in Finite Mixture of Semi-parametric Generalized Linear Models

Introduction Selection the appropriate statistical model for the response variable is one of the most important problem in the finite mixture of generalized linear models. One of the distributions which it has a problem in a finite mixture of semi-parametric generalized statistical models, is the Poisson distribution. In this paper, to overcome over dispersion and computational burden, finite ...