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Problems of finding confidence intervals (CIs) and prediction intervals (PIs) for two-parameter negative binomial distributions are considered. Simple CIs for the mean of a two-parameter negative binomial distribution based on some large sample methods are proposed and compared with the likelihood CIs. Proposed CIs are not only simple to compute, but also better than the likelihood CIs for moderate sample sizes. Prediction intervals for the mean of a future sample from a two-parameter negative binomial distribution are also proposed and evaluated for their accuracy. The methods are illustrated using two examples with real life data sets.

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The concept of fitness is central to evolution, but it quantifies only the expected number of offspring an individual will produce. The actual number of offspring is also subject to demographic stochasticity-that is, randomness associated with birth and death processes. In nature, individuals who are more fecund tend to have greater variance in their offspring number. Here, we develop a model for the evolution of two types competing in a population of nonconstant size. The fitness of each type is determined by pairwise interactions in a prisoner's dilemma game, and the variance in offspring number depends upon its mean. Although defectors are preferred by natural selection in classical population models, since they always have greater fitness than cooperators, we show that sufficiently large offspring variance can reverse the direction of evolution and favor cooperation. Large offspring variance produces qualitatively new dynamics for other types of social interactions, as well, which cannot arise in populations with a fixed size or with a Poisson offspring distribution.

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Binomial autoregressive models are frequently used for modeling bounded time series counts. However, they are not well developed for more complex bounded time series counts of the occurrence of n exchangeable and dependent units, which are becoming increasingly common in practice. To fill this gap, this paper first constructs an exchangeable Conway-Maxwell-Poisson-binomial (CMPB) thinning operator and then establishes the Conway-Maxwell-Poisson-binomial AR (CMPBAR) model. We establish its stationarity and ergodicity, discuss the conditional maximum likelihood (CML) estimate of the model's parameters, and establish the asymptotic normality of the CML estimator. In a simulation study, the boxplots illustrate that the CML estimator is consistent and the qqplots show the asymptotic normality of the CML estimator. In the real data example, our model takes a smaller AIC and BIC than its main competitors.

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Based on the well-known Poisson (P) distribution and the new generalized Lindley distribution (NGLD) developed by using gamma (α,θ) and gamma (α-1,θ) distributions, a new compound two-parameter Poisson generalized Lindley (TPPGL) distribution is proposed in this paper and thereon systematically explores the mathematical properties. Closed form expressions are assembled for such properties including the probability generating function, moments, skewness, kurtosis, etc. The likelihood-based method is used for estimating the parameters followed by a broad Monte Carlo simulation study. To further motivate the proposed model, a count regression model and a first order integer valued autoregressive process are constructed based on the novel TPPGL distribution. The empirical importance of the proposed models is confirmed through application to four real datasets.

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Transmission of Ross River virus (RRV) is influenced by climatic, environmental, and socio-economic factors. Accurate and robust predictions based on these factors are necessary for disease prevention and control. However, the complicated transmission cycle and the characteristics of RRV notification data present challenges. Studies to compare model performance are lacking. In this study, we used RRV notification data and exposure data from 2001 to 2020 in Queensland, Australia, and compared ten models (including generalised linear models, zero-inflated models, and generalised additive models) to predict RRV incidence in different regions of Queensland. We aimed to compare model performance and to evaluate the effect of statistical over-dispersion and zero-inflation of RRV surveillance data, and non-linearity of predictors on model fit. A variable selection strategy for screening important predictors was developed and was found to be efficient and able to generate consistent and reasonable numbers of predictors across regions and in all training sets. Negative binomial models generally exhibited better model fit than Poisson models, suggesting that over-dispersion in the data is the primary factor driving model fit compared to non-linearity of predictors and excess zeros. All models predicted the peak periods well but were unable to fit and predict the magnitude of peaks, especially when there were high numbers of cases. Adding new variables including historical RRV cases and mosquito abundance may improve model performance. The standard negative binomial generalised linear model is stable, simple, and effective in prediction, and is thus considered the best choice among all models.

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Inflated data and over-dispersion are two common problems when modeling count data with traditional Poisson regression models. In this study, we propose a latent class inflated Poisson (LCIP) regression model to solve the unobserved heterogeneity that leads to inflations and over-dispersion. The performance of the model estimation is evaluated through simulation studies. We illustrate the usefulness of introducing a latent class variable by analyzing the Behavioral Risk Factor Surveillance System (BRFSS) data, which contain several excessive values and characterized by over-dispersion. As a result, the new model we proposed displays a better fit than the standard Poisson regression and zero-inflated Poisson regression models for the inflated counts.

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Pathogen exposure to multiple hurdles could result in variation in the number of survivors, which needs to be carefully considered using appropriate regression models for dealing with survivor dispersion. The aim of this study was to evaluate the impact of the hurdles on the random component of the measured variation and on its unexplained part (over or under-dispersion) representing the departure from randomness, i.e. non-randomness, in survivors of a multi-strain mixture of L. monocytogenes. The pathogen inactivation curves were fitted to the Weibull model within the Conway-Maxwell-Poisson process. In all the 20 hurdle combinations, the surviving cells, whether they showed an upward curvature or linear kinetics, displayed the randomness revealed by the degree of dispersion of the inactivation parameters (-b and p). In 15 combinations, a significant dispersion coefficient (c0), which reflected the non-random component of variation was evident, denoting either over-dispersion (c0 > 0 in 13 combinations) or under-dispersion (c0 < 0 in 2 combinations). The observed dependence of the under- and over-dispersion conditions on the inactivation rate was confirmed by a Monte Carlo simulation based on the inactivation parameter -b. Including both randomness and non-randomness provides a more accurate estimation of survivors, which certainly impacts on intervention practices.

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Recently developed actigraphy devices have made it possible for continuous and objective monitoring of sleep over multiple nights. Sleep variables captured by wrist actigraphy devices include sleep onset, sleep end, total sleep time, wake time after sleep onset, number of awakenings, etc. Currently available statistical methods to analyze such actigraphy data have limitations. First, averages over multiple nights are used to summarize sleep activities, ignoring variability over multiple nights from the same subject. Second, sleep variables are often analyzed independently. However, sleep variables tend to be correlated with each other. For example, how long a subject sleeps at night can be correlated with how long and how frequent he/she wakes up during that night. It is important to understand these inter-relationships. We therefore propose a joint mixed effect model on total sleep time, number of awakenings, and wake time. We develop an estimating procedure based upon a sequence of generalized linear mixed effects models, which can be implemented using existing software. The use of these models not only avoids computational intensity and instability that may occur by directly applying a numerical algorithm on a complicated joint likelihood function, but also provides additional insights on sleep activities. We demonstrated in simulation studies that the proposed estimating procedure performed well in estimating both fixed and random effects' parameters. We applied the proposed model to data from the Women's Interagency HIV Sleep Study to examine the association of employment status and age with overall sleep quality assessed by several actigraphy measured sleep variables.

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In the framework of the study of Siluriform fish monogeneans of Lake Tanganyika, we described two new species of Bagrobdella from Auchenoglanis occidentalis, Bagrobdella vanhovei sp. nov. is characterized by the morphology of its MCO which is unique (terminal opening) and Bagrobdella vansteenbergei sp. nov. characterized by the size of its hooks, which are almost all of the same size, and its male copulating organ with a unique shape: sub-terminal opening and no membrane surrounding.

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Predicting pedestrian crashes on urban roads is one of the most important issues related to urban traffic safety. Due to the lack of spatial correlation and instability in the crash data, the statistical reliability of Empirical Bayesian method in the combination of the observed and predicted crash frequency is questionable. In this study, an EB model has been developed to estimate the expected frequency of pedestrian crashes in urban areas using the over-dispersion parameter taking into account the spatial correlation of crash data. The objective of this study is to estimate the expected geographical frequency of pedestrian crashes using the Empirical Bayesian (EB) approach using weighted geographical regression models for pedestrian crashes in Tehran. For doing so, four models of geographic weighted Poisson regression (GWPR), geographic weighted zero-inflated Poisson regression (GWZIPR), geographic weighted Negative Binomial regression (GWNBR) and the geographic weighted zero-inflated Negative Binomial regression (GWZINBR) have been used. In this study, the areas analyzed for the development of the EB model based on pedestrian exposure variables include traffic analysis zones (TAZs). Finally, the EB model was extended to the Geographic Empirical Bayesian (Ge-EB) model. The results showed that GWZIPR and GWZINBR models make more accurate predictions. These models had the lowest values of Akaike Information Criterion (AIC), the lowest values of Cross Validation and the lowest values of Root Mean Square Error (RMSE). The Moran and Variance Inflated Factor (VIF) indices were also within acceptable limits. The weighted negative binomial distribution could moderate the amount of heterogeneity of crash data to some extent. This study has shown the dispersion and density of pedestrian crashes without having the volume of pedestrians and thus can be done by taking safety measures in places prone to pedestrian crashes.

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This article provides a thorough explanation of methods and theoretical concepts to detect infectivity of COVID-19. The concept of heterogeneity is discussed and its impacts on COVID-19 pandemics are explored. Observable heterogeneity is distinguished from non-observable heterogeneity. The data support the concepts of heterogeneity and the methods to extract and interpret the data evidence for the conclusions in this paper. Heterogeneity among the vulnerable to COVID-19 is a significant factor in the contagion of COVID-19, as demonstrated with incidence rates using data of a Diamond Princess cruise ship. Given the nature of the pandemic, its heterogeneity with different social norms, pre- and post-voyage quick testing procedures ought to become the new standard for cruise ship passengers and crew. With quick testing, identification of those infected and thus, not allowing to embark on a cruise or quarantine those disembarking, and other mitigation strategies, the popular cruise adventure could become norm for safe voyage. The novel method used in this article adds valuable insight in the modeling of disease and specifically, the COVID-19 virus.

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In employing spatial regression models for counts, we usually meet two issues. First, the possible inherent collinearity between covariates and the spatial effect could lead to misleading inferences. Second, real count data usually reveal over- or under-dispersion where the classical Poisson model is not appropriate to use. We propose a flexible Bayesian hierarchical modeling approach by joining nonconfounding spatial methodology and a newly reconsidered dispersed count modeling from the renewal theory to control the issues. Specifically, we extend the methodology for analyzing spatial count data based on the gamma distribution assumption for waiting times. The model can be formulated as a latent Gaussian model, and consequently, we can carry out the fast computation by using the integrated nested Laplace approximation method. We examine different popular approaches for handling spatial confounding and compare their performances in the presence of dispersion. Two real applications from a crime study against women in India as well as stomach cancer incidences in Slovenia motivate the suggested methods. We also perform a simulation study to understand the proposed approach's merits better. Supplementary Materials for this article are available.

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For count data, though a zero-inflated model can work perfectly well with an excess of zeroes and the generalized Poisson model can tackle over- or under-dispersion, most models cannot simultaneously deal with both zero-inflated or zero-deflated data and over- or under-dispersion. Ear diseases are important in healthcare, and falls into this kind of count data. This paper introduces a generalized Poisson Hurdle model that work with count data of both too many/few zeroes and a sample variance not equal to the mean. To estimate parameters, we use the generalized method of moments. In addition, the asymptotic normality and efficiency of these estimators are established. Moreover, this model is applied to ear disease using data gained from the New South Wales Health Research Council in 1990. This model performs better than both the generalized Poisson model and the Hurdle model.

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BACKGROUND: The ability of mercury to deposit throughout the body and alter a wide range of molecular and cellular pathways results in a polymorphic and complex clinical phenotype with over 250 possible symptoms. However, some of them are recurrently cited as evoking chronic mercury poisoning. In this light, dentists users of dental amalgams are chronically exposed to mercury so that in-depth epidemiological investigations and adapted statistical methods are required to highlight adverse effects of this exposure. METHODS: In order to study the health impact of the occupational mercury exposure in a population of liberal dentists practicing in two Moroccan regions, a list of eighteen subjective symptoms commonly associated with micro-hydrargyrism was drawn up. Then, seven statisctical models adapted to count data were fitted. Finally, three methods were used to compare their relative performance in order to choose the most appropriate one. RESULTS: The adopted logical path, from the response variable selection till models' comparison, led us to lean towards quasi-Poisson regression as the best way to predict the number of symptoms declared by dentists according to mercury exposure. CONCLUSIONS: Interpretation of the selected model allowed us to conclude that the reduction of dental amalgam use allows the reduction of subjective symptoms related to mercury exposure.

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BACKGROUND: Histone modification constitutes a basic mechanism for the genetic regulation of gene expression. In early 2000s, a powerful technique has emerged that couples chromatin immunoprecipitation with high-throughput sequencing (ChIP-seq). This technique provides a direct survey of the DNA regions associated to these modifications. In order to realize the full potential of this technique, increasingly sophisticated statistical algorithms have been developed or adapted to analyze the massive amount of data it generates. Many of these algorithms were built around natural assumptions such as the Poisson distribution to model the noise in the count data. In this work we start from these natural assumptions and show that it is possible to improve upon them. RESULTS: Our comparisons on seven reference datasets of histone modifications (H3K36me3 & H3K4me3) suggest that natural assumptions are not always realistic under application conditions. We show that the unconstrained multiple changepoint detection model with alternative noise assumptions and supervised learning of the penalty parameter reduces the over-dispersion exhibited by count data. These models, implemented in the R package CROCS ( https://github.com/aLiehrmann/CROCS ), detect the peaks more accurately than algorithms which rely on natural assumptions. CONCLUSION: The segmentation models we propose can benefit researchers in the field of epigenetics by providing new high-quality peak prediction tracks for H3K36me3 and H3K4me3 histone modifications.

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This paper introduces a first-order integer-valued autoregressive process with a new innovation distribution, shortly INARPQX(1) process. A new innovation distribution is obtained by mixing Poisson distribution with quasi-xgamma distribution. The statistical properties and estimation procedure of a new distribution are studied in detail. The parameter estimation of INARPQX(1) process is discussed with two estimation methods: conditional maximum likelihood and Yule-Walker. The proposed INARPQX(1) process is applied to time series of the monthly counts of earthquakes. The empirical results show that INARPQX(1) process is an important process to model over-dispersed time series of counts and can be used to predict the number of earthquakes with a magnitude greater than four.

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Species' evolutionary histories shape their present-day ecologies, but the integration of phylogenetic approaches in ecology has had a contentious history. The field of ecophylogenetics promised to reveal the process of community assembly from simple indices of phylogenetic pairwise distances - communities shaped by environmental filtering were composed of closely related species, whereas communities shaped by competition were composed of less closely related species. However, the mapping of ecology onto phylogeny proved to be not so straightforward, and the field remains mired in controversy. Nonetheless, ecophylogenetic methods provided important advances across ecology. For example the phylogenetic distances between species is a strong predictor of pest and pathogen sharing, and can thus inform models of species invasion, coexistence and the disease dilution/amplification effect of biodiversity. The phylogenetic structure of communities may also provide information on niche space occupancy, helping interpret patterns of facilitation, succession and ecosystem functioning - with relevance for conservation and restoration - and the dynamics among species within foodwebs and metacommunities. I suggest leveraging advances in our understanding of the process of evolution on phylogenetic trees would allow the field to progress further, while maintaining the essence of the original vision that proved so seductive.

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Background. Under-five mortality has continued a key challenge to public health in Ethiopia, and other sub-Saharan Africa countries. The threat of under-five mortality is incessant and more studies are needed to generate new scientific evidence. This study aimed to model the number of under-five deaths a mother has experienced in her lifetime and factors associated with it in Ethiopia. Method. A retrospective cross-sectional study based on data obtained from the Ethiopian Demographic and Health Survey (DHS), 2016 was used. The response variable was the total number of under-five children died per mother in her lifetime. Variables such as maternal socioeconomic and demographic characteristics, health, and environmental factors were considered as risk factors of under-five mortality. Hurdle negative binomial (HNB) regression analysis was employed to determine the factors associated with under-five mortality. Results. The data showed that 27.2% (95%CI: 0263, 0.282) of women experienced under-five deaths. The study revealed the age of mother at first birth, the age of mother at the time of under-five mortality occurred, number of household members, household access to electricity, region, educational level of the mother, sex of household head, wealth index, mother residing with husband/partner at the time of under-five mortality occurred as factors associated with under-five mortality. Age of mother at first birth 18 to 24 (IRR = .663; 95%CI: 0.587, 0.749), 25 or higher years old (IRR = 0.424; 95%CI: 0.306, 0.588), access to electricity (IRR = 0.758; 95%CI: 0.588, 0.976), primary education level of the mother (IRR = 0.715; 95%CI: 0.584, 0.875) and the richer wealth index (IRR = 0.785; 95%CI: 0.624, 0.988) were associated with reduced incidence of under-five mortality controlling for other variables in the model. Whereas older age of mother 35 to 39 (IRR = 5.252; 95%CI: 2.992, 9.218), 40 to 44 (IRR = 7.429; 95%CI: 4.188, 13.177), 45 to 49 (IRR = 8.697; 95%CI: 4.853, 15.585), being a resident of the Benishangul-gumuz region (IRR = 1.781; 95%CI: 1.303, 2.434), female household head (IRR = 1.256; 95%CI: 1.034, 1.525) were associated with an increased incidence of under-five mortality. Conclusion. The findings suggested that early age of mothers' at first birth and old ages of mothers', female household head and being uneducated were found to increase the incidence of the under-five mortality, whereas access to electricity and living with husband was statistically associated with reduced incidence of under-five mortality. The implication of this study is that policymakers and stakeholders should provide health education for mothers not to give birth at an earlier age and improve living standards to achieve sustainable development goals.

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In this paper, a new two-parameter discrete distribution is introduced. It belongs to the family of the weighted geometric distribution (GD), with the feature of using a particular trigonometric weight. This configuration adds an oscillating property to the former GD which can be helpful in analyzing the data with over-dispersion, as developed in this study. First, we present the basic statistical properties of the new distribution, including the cumulative distribution function, hazard rate function and moment generating function. Estimation of the related model parameters is investigated using the maximum likelihood method. A simulation study is performed to illustrate the convergence of the estimators. Applications to two practical datasets are given to show that the new model performs at least as well as some competitors.

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A quantitative probabilistic model was developed to estimate the concentration of Listeria monocytogenes in cooked meat products based on presence/absence data and an assumed zero-inflated distribution, i.e. zero-inflated Poisson (ZIP) or zero-inflated Poisson lognormal (ZIPL) distribution. The performance of these two distributions was compared in two data sets (data set A and B), which represented L. monocytogenes prevalence and concentrations in cooked meat products. In this study, L. monocytogenes contamination data consisted of 4.23% (8/189) and 4.17% (5/120) non-zero counts for data set A and B, respectively. The contamination level of L. monocytogenes, determined by the most probable number (MPN) technique, ranged from 3 to 93 MPN/g among 13 positive samples. The goodness-of-fit test indicated that the ZIPL distribution was better than the simpler ZIP distribution, when L. monocytogenes contamination levels on positive cooked meat samples illustrated large heterogeneity. Results obtained from ZIPL distribution showed that the logarithmic mean value of L. monocytogenes positive samples was 1.5 log MPN/g (log σ = 0.4) for data set A and B. This study provides an alternative probabilistic method when only qualitative data is available in Quantitative microbial risk assessment (QMRA), in particular if pathogen concentrations consist of large numbers of zero counts and represent high variability.

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