Thesis (Ph. D.)--Virginia Polytechnic Institute, 1963. / Vita. Abstract. Includes bibliographical references (leaves 124-126). Also available via the Internet.

Analysis of Variance (ANOVA) is the easiest and most widely used model nowadays in statistics. ANOVA however requires a set of assumptions for the model to be a valid choice and for the inferences to be accurate. Among many, ANOVA assumes the data in question is normally distributed and homogenous. However, data from most disciplines does not meet the assumption of normality and/or equal variance. Regrettably, researchers do not always check whether the assumptions are met, and if these assumptions are violated, inferences might well be wrong. We conducted a simulation study to compare the performance of standard ANOVA to Poisson and Negative Binomial models when applied to counts data. We considered different combination of sample sizes and underlying distributions. In this simulation study, we first assed Type I error for each model involved. We then compared power as well as the quality of the estimated parameters across the models.

<p>Syftet med uppsatsen är att försöka förklara vad det är som påverkar tiden som en mamma ammar. För att undersöka vad det är som påverkar tiden som en mamma ammar, har en Zero inflated negative binomial-modell (ZINB-modell) tagits fram. Resultaten visar att det som avgör hur länge en mamma kommer att amma är: Graviditetens längd, mammans ålder, mammans rökvanor under graviditetens sista månader, mammans rökvanor samt mammans nationella ursprung.</p>

Syftet med uppsatsen är att försöka förklara vad det är som påverkar tiden som en mamma ammar. För att undersöka vad det är som påverkar tiden som en mamma ammar, har en Zero inflated negative binomial-modell (ZINB-modell) tagits fram. Resultaten visar att det som avgör hur länge en mamma kommer att amma är: Graviditetens längd, mammans ålder, mammans rökvanor under graviditetens sista månader, mammans rökvanor samt mammans nationella ursprung.

Many state agencies consider exclusive truck facilities to be an alternative to handle the safety and operational issues due to the increasing truck volumes. No such facilities exist, and there are no standard tools or procedures for measuring safety performance of an exclusive truck facility. This thesis aims at identifying factors that affect truck crashes, whose results could be used for better designing exclusive truck facilities. To accomplish the objectives of this thesis, five years’ roadway and crash data for Texas was collected to develop a comprehensive crash database. Negative binomial regression models were used to establish a relationship between truck crashes and various environmental, geometric and traffic variables. Separate models were developed for truck-related (involving at least one truck and another vehicle), truck-only (two trucks or more) and single-truck crashes. The results suggested that the percentage of trucks in Average Annual Daily Traffic (AADT), classification of the roadway (Rural/Urban), posted speed limit, surface condition, alignment and shoulder width are associated with truck crashes. It was observed that truck-related and truck-only crashes decreased as the percentage of trucks increased on freeway facilities. Based on conclusions derived from the literature review and statistical analyses, straight segments with wider shoulders and uniform grades are recommended for exclusive truck facilities. It is also recommended to provide ramps, horizontal and vertical curvature and signing based on truck size, driver eye height, braking ability and maneuverability. These models were developed using mixed-flow traffic data to understand the association of various factors with truck crashes. These models should not be used directly to estimate or predict truck crashes. Further analysis with more detailed data under different flow conditions might help in quantifying the safety performance of exclusive truck facilities.

Many state agencies consider exclusive truck facilities to be an alternative to handle the safety and operational issues due to the increasing truck volumes. No such facilities exist, and there are no standard tools or procedures for measuring safety performance of an exclusive truck facility. This thesis aims at identifying factors that affect truck crashes, whose results could be used for better designing exclusive truck facilities. To accomplish the objectives of this thesis, five years' roadway and crash data for Texas was collected to develop a comprehensive crash database. Negative binomial regression models were used to establish a relationship between truck crashes and various environmental, geometric and traffic variables. Separate models were developed for truck-related (involving at least one truck and another vehicle), truck-only (two trucks or more) and single-truck crashes. The results suggested that the percentage of trucks in Average Annual Daily Traffic (AADT), classification of the roadway (Rural/Urban), posted speed limit, surface condition, alignment and shoulder width are associated with truck crashes. It was observed that truck-related and truck-only crashes decreased as the percentage of trucks increased on freeway facilities. Based on conclusions derived from the literature review and statistical analyses, straight segments with wider shoulders and uniform grades are recommended for exclusive truck facilities. It is also recommended to provide ramps, horizontal and vertical curvature and signing based on truck size, driver eye height, braking ability and maneuverability. These models were developed using mixed-flow traffic data to understand the association of various factors with truck crashes. These models should not be used directly to estimate or predict truck crashes. Further analysis with more detailed data under different flow conditions might help in quantifying the safety performance of exclusive truck facilities.

This research assesses the performance of over-dispersed Poisson regression model and negative binomial model with count data. It examines the association between price plan features of mobile phone services and the number of people who adopt the plan. Mobile service data is used to estimate the model with a sample of one million customers running from February 2006 to September 2009. Under three main categories, customer type, age, and handset price, we run the model based on price plan features. Estimates are derived from the maximum likelihood estimation (MLE) method. Root mean squared error (RMSE) is used to observe the statistical fits of all the regression models. Then, we construct four estimation and holdout samples, leaving out one, three, six, and twelve months. The estimation constitutes the in-sample (IS) and the holdout represents the out-sample (OS). By estimating the IS, we predict the OS. Root mean squared error of prediction (RMSEP) is checked to see how accurate the prediction is. Results generally suggest that academic year start (AYS), seasonality, duration of months since launch of price plan (DMLP), basic fees, rate with no discount (RND), free call minutes (FCM), free data (FD), free text messaging (FTM), free perk rating (FPR), and handset support all show significant effect. The significance occurs depending on the segment. The RMSE and RMSEP show that the over-dispersed Poisson model outperforms the negative binomial model. Further implications and limitations of the results are discussed. / text

As one of the major data analysis methods, statistical models play an important role in traffic safety analysis. A common situation associated with crash data is the phenomenon known as overdispersion which has been discussed and investigated frequently in recent years. As such, researchers have proposed several models, such as the Poisson Gamma (PG) or Negative Binomial (NB), the Poisson-lognormal, or the Poisson-Weibull, to handle the overdispersion. Unfortunately, very few models have been proposed for specifically analyzing the sources of dispersions in the data. Better understanding of sources of variation and overdispersion could help in managing safety, such as establishing relationships and applying appropriate treatments or countermeasures, more efficiently. Given the limitations of existing models for exploring the source of overdispersion of crash data, this research examined a new model function that could be applied to explore sources of extra variability through the use of the Generalized Waring (GW) models. This model, which was recently introduced by statisticians, divides the observed variability into three components: randomness, internal differences between road segments or intersections, and the variances caused by other external factors that have not been included as covariates in the model. To evaluate these models, GW models were examined using both simulated and empirical crash datasets, and the results were compared to the most commonly used NB model and the recently developed NB-Lindley models. For model parameter estimation, both the maximum likelihood method and a Bayesian approach were adopted for better comparison. A simulation study was used to show the better performance of this model compared to NB model for overdispersed data, and then an application in the empirical crash data illustrates its capability of modeling data sets with great accuracy and exploring the source of overdispersion. The performances of hotspot identification for these two kinds of models (i.e., GW models and NB models) were also examined and compared based on the estimated models from the empirical dataset. Finally, bias properties related to the choice of prior distributions for parameters in GW model were examined by using a simulation study. In addition, the suggestions on the choice of minimum sample size and priors were presented for different kinds of datasets.

The models for volatility, autoregressive conditional heteroscedastic (ARCH) and generalized autoregressive conditional heteroscedastic (GARCH) are discussed. Stationarity condition and forecasting for simple ARCH(1) and GARCH(1,1) models are given. The model for discrete time series is proposed to be negative binomial integer-valued GARCH model, which is a generalization of the Poisson INGARCH model. The stationarity conditions and the autocorrelation function are given. For parameter estimation, three methodologies are presented with a focus on maximum likelihood approach. Simulation study on a sample size of 100 and 500 are carried out and the results are presented. An application of the model to a real time series with numerical example is given indicating that the proposed methodology performs better than the Poisson and double Poisson model-based methods.

Resumo: O estudo da distribuição espacial de pragas é fundamental para elaboração de planos de amostragem para uso no manejo integrado de pragas. Para Toxoptera citricida foi estudada a distribuição espacial em talhões de pomares de citros comerciais de laranja (Citrus sinensis) da variedade Pêra, com 5, 9 e 15 anos de idade, durante o período de setembro de 2004 a abril de 2005. Foram realizadas 14 amostragens de número de pulgões-preto em intervalos aproximados de 15 dias entre as mesmas, utilizando-se armadilhas adesivas de cor amarela (0,11 x 0,11 m) fixadas à planta a 1,5 m de altura aproximadamente. As armadilhas foram distribuídas na área, a cada cinco plantas na linha, em linhas alternadas, totalizando 137 armadilhas no talhão com 5 anos, 140 no talhão com 9 anos e 80 no talhão com 15 anos. A lei de Taylor e a distribuição binomial negativa foram os modelos que melhor representaram a distribuição da população. Foram com construídos planos de amostragens para levantamento desta praga com base na lei de Taylor e na distribuição binomial negativa. / Abstract: The study of spatial distribution of insects is fundamental to elaborate sampling plans with potential to use in integrated pest management. The spatial distribution of Toxoptera citricida was studied in plots of commercial orchards of orange (Citrus sinensis) of the variety 'Pêra' with 5, 9 and 15 years of age, during the period of September of 2004 and April of 2005. Fourteen samples of the number of Toxoptera citricida was performed each 15d approximately, using yellow adhesive traps fixed at 1,5 m of height each 5 plants in alternated lines, summing 137 traps in the 5-years plot, 140 traps in the 9-years plot and 80 traps in the 15-years plot. The best models fitted the distribution of population were the Taylor Law and negative binomial distribution, which were used to elaborate the sampling plans. / Orientador: José Carlos Barbosa / Coorientador: Pedro Takao Yamamoto / Banca: Antonio Carlos Busoli / Banca: Wilson Itamar Maruyama / Mestre