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We define the class of bivariate binomial distributions as Poisson distributions transformed by a binomial dilution and mixing with a gamma distribution. They are used to study the number of nematodes, considering the sex ratio, parasitizing birds.

When one arm in a trial has a worse early endpoint such as recurrence, a data-monitoring committee might recommend that all participants are offered the apparently superior treatment. The resultant crossover makes it difficult to measure differences between arms thereafter, including for longer-term endpoints such as mortality and disease-specific mortality. In this paper, we consider estimator...

BACKGROUND Infection with multiple types of human papillomavirus (HPV) is one of the main risk factors associated with the development of cervical lesions. In this study, cervical samples collected from 1,810 women with diverse sociocultural backgrounds, who attended to their cervical screening program in different geographical regions of Colombia, were examined for the presence of cervical les...

Next-generation sequencing technologies now constitute a method of choice to measure gene expression. Data to analyze are read counts, commonly modeled using negative binomial distributions. A relevant issue associated with this probabilistic framework is the reliable estimation of the overdispersion parameter, reinforced by the limited number of replicates generally observable for each gene. M...

The FBI has reported the number of monthly firearm background checks in every state since November 1998. This article uses data on background checks at the state level to explore the relationship between guns and crime. The background checks capture an individual s intention to purchase a firearm and explain 96% of the variation in gun manufacturing at a national level. Fixed effect negative bi...

The problem of inference about the binomial N parameter is considered. Applications arise in situations where an unknown population size is to be estimated. Previous work has focused on point estimation, but many applications require interval estimation, prediction, and decision-making. A Bayes empirical Bayes approach is presented. This provides a simple and flexible way of specifying prior in...

RNA sequencing (RNA-Seq) enables the measurement and comparison of gene expression with isoform-level quantification. Differences in the effect of each isoform may make traditional methods, which aggregate isoforms, ineffective. Here, we introduce a variance component-based test that can jointly test multiple isoforms of one gene to identify differentially expressed (DE) genes, especially those...

We consider Kemp’s q-analogue of the binomial distribution. Several convergence results involving the classical binomial, the Heine, the discrete normal, and the Poisson distribution are established. Some of them are q-analogues of classical convergence properties. From the results about distributions, we deduce some new convergence results for (q-)Krawtchouk and q-Charlier polynomials. Besides...

Frank's observation that a TEM bright-field image acquired under non-stationary conditions can be modeled by the time integral of the standard TEM image model [J. Frank, Nachweis von objektbewegungen im lichtoptis- chen diffraktogramm von elektronenmikroskopischen auf- nahmen, Optik 30 (2) (1969) 171-180.] is re-derived here using counting statistics based on Poisson's binomial distribution. Th...