Traditional techniques for calculating control limits for processes with discrete responses are based on the Poisson distribution. However, for many processes, the assumption of a Poisson distribution is violated. In such cases, use of traditional Poisson control limits may result in an inflated risk of Type I error. The negative binomial distribution is a natural extension of the Poisson distr...

In this paper we address the class of anti-uniform Huffman (AUH) codes, named also unary codes, for sources with finite and infinite alphabet, respectively. Geometric, quasi-geometric, Fibonacci, exponential, Poisson, and negative binomial distributions lead to anti – uniform sources for some ranges of their parameters. Huffman coding of these sources results in AUH codes. We prove that as resu...

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 are too heavy-tailed to be fitted over their entire ranges by Poisson or negative binomial distributions which would be expected for uncorrelated proc...

Field infestation and spatial distribution of introduced Bactrocera carambolae Drew and Hancock and native species of Anastrepha in common guavas [Psidium guajava (L.)] were investigated in the eastern Amazon. Fruit sampling was carried out in the municipalities of Calçoene and Oiapoque in the state of Amapá, Brazil. The frequency distribution of larvae in fruit was fitted to the negative binom...

The negative binomial distribution becomes highly skewed under extreme dispersion. Even at moderately large sample sizes, the sample mean exhibits a heavy right tail. The standard normal approximation often does not provide adequate inferences about the data’s expected value in this setting. In previous work, we have examined alternative methods of generating confidence intervals for the expect...

Cystic echinococcosis, caused by Echinococcus granulosus, is an emerging disease in many parts of the world and, in particular, in eastern Europe and the former Soviet Union. This paper examines the abundance of infection of E. granulosus in the definitive host in southern Kazakhstan. Observed data are fitted to a mathematical model in order to decide if the parasite population is partly regula...

Spatial distributions of several species of plant-parasitic nematodes were determined in each of three fallow vegetable fields and in smaller subunits of those fields. Goodness of fit to each of several theoretical distributions was tested hy means of a X(2) test. Distributions for most species showed good agreement with a negative binomial model. An exception occurred with Crictmemella sp., wh...

It is crucial for researchers to optimize RNA-seq experimental designs for differential expression detection. Currently, the field lacks general methods to estimate power and sample size for RNA-Seq in complex experimental designs, under the assumption of the negative binomial distribution. We simulate RNA-Seq count data based on parameters estimated from six widely different public data sets (...

Assessment of treatment efficacy in metastatic castration-resistant prostate cancer (mCRPC) is limited by frequent nonmeasurable bone metastases. The count of circulating tumor cells (CTCs) is a promising surrogate marker that may replace the widely used prostate-specific antigen (PSA). The purpose of this study was to quantify the dynamic relationships between the longitudinal kinetics of thes...

Newly reported normalized cumulant moments of charged particles in ee collisions by the SLD collaboration are analyzed by the truncated modified negative binomial distribution (MNBD) and the negative binomial distribution (NBD). Calculated result by the MNBD describes the oscillatory behavior of the data much better than that by the NBD. PACS number(s): 13.65.+i, 34.10.+x Normalized cumulant mo...