相关论文: H-function extension of the NBD in the light of ex…
The H-function extension of the Negative Binomial Distribution is investigated for scaling exponents mu<0. Its analytic form is derived via a convolution property of the H-function. Applications are provided using multihadron and galaxy…
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…
We analyze various data of multiplicity distributions by means of the Modified Negative Binomial Distribution (MNBD) and its KNO scaling function, since this MNBD explains the oscillating behavior of the cumulant moment observed in e^+e^-…
It is shown that simple extension of the modified negative binomial distribution describes negatively charged particle multiplicity distributions in e+e- annihilation, measured in the whole phase space, as well as the modified negative…
On the basis of a recently introduced generalization of the negative binomial distribution the influence of higher-order perturbative QCD effects on multiplicity fluctuations are studied for deep inelastic e^+p scattering at HERA energies.…
Oscillatory behavior of cumulant moments obtained from the experimental data in $pp$ collisions and $\bar{p}p$ collisions are analyzed by the modified negative binomial distribution (MNBD) and the negative binomial distribution (NBD). Both…
In this article, a generalized version of Negative binomial-beta exponential distribution with five parameters have been introduced. Some interesting submodels have been derived from it. A comprehensive mathematical treatment of proposed…
For multiple testing based on p-values with c\`{a}dl\`{a}g distribution functions, we propose an FDR procedure "BH+" with proven conservativeness. BH+ is at least as powerful as the BH procedure when they are applied to super-uniform…
In general, while obtaining the probability density function of sums and products of shifted random variables, ordinary analytical methods such as Fourier and Mellin transforms tend to provide integrals which cannot be expressed in terms of…
This paper introduces a new discrete distribution suggested by curtailed sampling rules common in early-stage clinical trials. We derive the distribution of the smallest number of independent Bernoulli(p) trials needed in order to observe…
The paper is devoted to study the $H$-function defined by the Mellin-Barnes integral $$H^{m,n}_{\thinspace p,q}(z)={\frac1{2\pi i}}\int_{\Lss} \HHs^{m,n}_{\thinspace p,q}(s)z^{-s}ds,$$ where the function $\HH^{m,n}_{\thinspace p,q}(s)$ is a…
We construct the hadronic multiplicity distribution in terms of an elementary distribution (at given impact parameter) and the inelastic overlap function characterized by the observed BEL (Blacker-Edgier-Larger) behaviour. With suitable…
The negative binomial distribution NB$(k,r)$ of Type I is the probability distribution for a sequence of independent Bernoulli trials (with success parameter $p\in(0,1)$) with $r$ nonoverlapping success runs of length $\ge k$. We present a…
In this paper we present an alternative representation of the Negative Binomial--Lindley distribution recently proposed by Zamani and Ismail (2010) which shows some advantages over the latter model. This new formulation provides a tractable…
The computation and inversion of the binomial and negative binomial cumulative distribution functions play a key role in many applications. In this paper, we explain how methods used for the central beta distribution function (described in…
Renormdynamic equations of motion and their solutions are given. New equation for NBD distribution and Riemann zeta function invented. Explicit forms of the z-Scaling functions are constructed.
As shown recently, one can obtain additional information from the measured multiplicity distributions, $P(N)$, by extracting the so-called modified combinants, $C_j$. This information is encoded in their specific oscillatory behavior, which…
Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation.…
The main aim of this present paper is to present a new extension of the fractional derivative operator by using the extension of Beta function recently defined by Shadab et al.[19]. Moreover, we establish some results related to the newly…
The negative binomial distribution (NBD) has been theorized to express a scale-invariant property of many-body systems and has been consistently shown to outperform other statistical models in both describing the multiplicity of…