Fractional derivative in time variable is introduced into the Fokker-Planck equation of a population growth model. It’s solution, the KNO scaling function, is transformed into the generating function for the multiplicity distribution. Formulas of the factorial moment and the Hj moment are derived from the generating function, which reduces to that of the negative binomial distribution (NBD), if...

In comparing the mean count of two independent samples, some practitioners would use the t-test or the Wilcoxon rank sum test while others may use methods based on a Poisson model. It is not uncommon to encounter count data that exhibit overdispersion where the Poisson model is no longer appropriate. This paper deals with methods for overdispersed data using the negative binomial distribution r...

BACKGROUND Dengue fever (DF) is a growing public health problem in Vietnam. The disease burden in Vietnam has been increasing for decades. In Hanoi, in contrast to many other regions, extrinsic drivers such as weather have not been proved to be predictive of disease frequency, which limits the usefulness of such factors in an early warning system. AIMS The purpose of this research was to revi...

A pure birth stochastic process with several initial conditions is considered. We analyze multiplicity distributions of e+e− collisions and e-p collisions, usig the Modified Negative Binomial Distribution (MNBD) and the Laguerre-type distribution. Several multiplicity distributions show the same minimum χ2’s values in analyses by means of two formulas: In these cases, we find that a parameter N...

Stochastic models are developed in this article to examine the rate of test misgrading in educational and psychological measurement. The estimation of inadvertent grading errors can serve as a basis for quality control in measurement. Limitations of traditional Poisson models have been reviewed to highlight the need to introduce new models using well established geometric and negative binomial ...

This paper focuses on the contribution of Australian Football League (AFL) players to their team's on-field network by simulating player interactions within a chosen team list and estimating the net effect on final score margin. A Visual Basic computer program was written, firstly, to isolate the effective interactions between players from a particular team in all 2011 season matches and, secon...

We analyse the distributions of the number of goals scored by home teams, away teams, and the total scored in the match, in domestic football games from 169 countries between 1999 and 2001. The probability density functions (PDFs) of goals scored cannot be fitted over their entire ranges by Poisson or negative binomial distributions; here, we compare the PDFs with those arising from extremal st...

Many species of microhymenopterous parasitoids have been registered on Phyllocnistis citrella, the citrus leafminer. The present study aimed to identify the spatial distribution pattern of the native and introduced parasitoids of P. citrella in two citrus orchards in Montenegro, RS. The new shoots from 24 randomly selected trees in each orchard were inspected at the bottom (0-1.5 m) and top (1....

In a multipath fading channel, the transmitted signal travels through several different paths to the receiver. In each path, amplitude and phase of the signal vary in a random manner. It is common to consider the number of paths as a large constant and to model random fluctuations of the phase by the uniform probability density function (PDF). However, these assumptions are not realistic in man...