Statistical Scrutiny of Particle Spectra in ep Collisions

Charged particle multiplicity distributions in positron–proton deep inelastic scattering at a centre-of-mass energy s = 300 GeV, measured in the hadronic centre-of-mass frames and in different pseudorapidity windows are studied in the framework of two statistical distributions, the shifted Gompertz distribution and the Weibull distribution. Normalised moments, normalised factorial moments and the H-moments of the multiplicity distributions are determined. The phenomenon of oscillatory behaviour of the counting statistics and the Koba-Nielsen-Olesen (KNO) scaling behaviour are investigated. This is the first such analysis using these data. In addition, projections of the two distributions for the expected average charged multiplicities obtainable at the proposed future ep colliders.

General Formulas for the Central and Non-Central Moments of the Multinomial Distribution

We present the first general formulas for the central and non-central moments of the multinomial distribution, using a combinatorial argument and the factorial moments previously obtained in Mosimann (1962). We use the formulas to give explicit expressions for all the non-central moments up to order 8 and all the central moments up to order 4. These results expand significantly on those in Newcomer (2008) and Newcomer et al. (2008), where the non-central moments were calculated up to order 4.

On refinements of the asymptotics expansion of the continuation of critical branching random processes

В настоящей работе для вероятности продолжения критических ветвящихся случайных процессов получено асимптотическое разложение в предположении о существовании факториальных моментов λk при k = 5, 6, . . . , m, m < ∞. In this paper, an asymptotic expansion is obtained for the probability of continuation of critical branching processes under the assumptions of the existence of factorial moments λk at k = 5, 6, . . . , m, m < ∞.

Negative binomial improved second degree lindley distribution and its application

The objective of this paper is to introduce a new two parameter mixed negative binomial distribution, namely negative binomial-improved second degree Lindley(NB-ISL) distribution. This distribution is obtained by mixing the negative binomial distribution with the improved second degree Lindley distribution. Many mixed distributions have been used in the literature for modeling the over dispersed count data, which provide a better fit compared to the Poisson and negative binomial distribution. In addition, we present the basic statistical properties of the new distribution such as factorial moments, mean and variance and the behavior of mean, variance and coefficient of variation are also discussed. Parameter estimation is implemented by using maximum likelihood estimation method. The performance of the NB-ISL distribution is shown in practice by applying it on real data set and compare it with some well-known count distributions. The result shows that the negative binomial-improved second degree Lindley distribution provides a better fit compared to Poisson, negative binomial and negative binomial-Lindley distributions.

Intermittency Study of Charged Particles Generated in Pb-Pb Collisions at sNN=2.76 TeV Using EPOS3

Charged particle multiplicity fluctuations in Pb-Pb collisions are studied for the central events generated using EPOS3 (hydro and hydro+cascade) at sNN=2.76 TeV. Intermittency analysis is performed in the midrapidity region in two-dimensional (η, ϕ) phase space within the narrow transverse momentum (pT) bins in the low pT region (pT≤1.0 GeV/c). Power-law scaling of the normalized factorial moments with the number of bins is not observed to be significant in any of the pT bins. Scaling exponent ν, deduced for a few pT bins, is greater than that of the value 1.304, predicted for the second-order phase transition by the Ginzburg-Landau theory. The link in the notions of fractality is also studied. Generalized fractal dimensions, Dq, are observed to decrease with the order of the moment q suggesting the multifractal nature of the particle generation in EPOS3.

A zero truncated discrete distribution: Theory and applications to count data

The analysis and modeling of zero truncated count data is of primary interest in many elds such as engineering, public health, sociology, psychology, epidemiology. Therefore, in this article we have proposed a new and simple structure model, named a zero truncated discrete Lindley distribution. Thedistribution contains some submodels and represents a two-component mixture of a zero truncated geometric distribution and a zero truncated negative binomial distribution with certain parameters. Several properties of the distribution are obtained such as mean residual life function, probability generating function, factorial moments, negative moments, moments of residual life function, Bonferroni and Lorenz curves, estimation of parameters, Shannon and Renyi entropies, order statistics with the asymptotic distribution of their extremes and range, a characterization, stochastic ordering and stress-strength parameter. Moreover, the collective risk model is discussed by considering theproposed distribution as primary distribution and exponential and Erlang distributions as secondary ones. Test and evaluation statistics as well as three real data applications are considered to assess the peformance of the distribution among the most frequently zero truncated discrete probability models.