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1
Ibukun, Michael Abimbola. "Modely s Touchardovým rozdělením." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-445468.
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In 2018, Raul Matsushita, Donald Pianto, Bernardo B. De Andrade, Andre Cançado & Sergio Da Silva published a paper titled ”Touchard distribution”, which presented a model that is a two-parameter extension of the Poisson distribution. This model has its normalizing constant related to the Touchard polynomials, hence the name of this model. This diploma thesis is concerned with the properties of the Touchard distribution for which delta is known. Two asymptotic tests based on two different statistics were carried out for comparison in a Touchard model with two independent samples, supported by simulations in R.
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Soares, Maria João de Sousa. "An avian relative fatality risk index for Iberian species on wind farms based on zero inflated count models." Master's thesis, Universidade de Aveiro, 2014. http://hdl.handle.net/10773/13866.
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Mestrado em Biologia AplicadaClimate change is one of the greatest threats towards humankind and wildlife. This consciousness motivated the search for alternatives that could contribute to mitigate climate change. Betting on renewable energies seems to be a winning strategy adopted worldwide in order to reduce greenhouse gas emissions responsible for global climate alterations and to improve nations’ energy independency. However, nowadays, these energy usages still have negative impacts, mostly on wildlife. Wind energy is even considered the greatest unintended human impact on avifauna. In this context, the aim of this thesis was to increase the knowledge about wind farms impacts on avifauna, which variables influence birds’ fatalities by collision with wind turbines and birds’ vulnerability. Models based on excessive zero counts were tested to understand which variables influence birds’ fatalities assessed on 25 Portuguese wind farms. This allowed to estimate the probability of mortality observation per species. The information obtained was used to build the fatality risk index that also considered the vulnerability factors, which give information of species conservation concern and resilience. Those indexes allow to prioritise the existing and limited conservation efforts on more vulnerable species. Models and indexes are also important for improving knowledge about wind energy impacts on wildlife and what can lead to reduce them, in order to achieve a sustainable and greener future.
As alterações climáticas são uma das maiores ameaças para a Humanidade e para a vida selvagem. A consciência sobre a importância destas questões motivou a procura de alternativas, com intuito de mitigar estas alterações globais, causadas nomeadamente pelos gases de efeitos de estufa. Assim, as energias renováveis apresentam-se como uma possível estratégia vencedora a adotar, de forma a reduzir as emissões destes gases e levar à independência energética. No entanto, o uso destas energias renováveis ainda apresenta impactes negativos, especialmente para os ecossistemas. A energia eólica é inclusivamente considerada uma das maiores causas não intencionais de origem antropogénica para a mortalidade adicional de aves. Neste contexto, esta dissertação tem como os principais objetivos o desenvolvimento do conhecimento relativo aos impactes da energia eólica, quais as variáveis que influenciam a mortalidade de aves respeitante à colisão com as turbinas eólicas assim como as variáveis que afetam a vulnerabilidade das espécies. Foram testados modelos de contagem com excesso de zeros para compreender a influência das variáveis nas observações de mortalidade em 25 parques eólicos portugueses. A partir destes modelos foi possível estimar a probabilidade de observação de mortalidade para cada uma das espécies estudadas, provocada por colisão com eólicas. Esta informação foi ainda utilizada de forma a desenvolver um índice de risco de fatalidade com base nestas estimativas, assim como em fatores elucidativos da vulnerabilidade das espécies, nomeadamente o seu estatuto de conservação e resiliência. Desta forma é então possível direcionar esforços e recursos para a preservação das espécies com maior vulnerabilidade e prioridade de conservação. Este tipo de modelos e índices é ainda fundamental para incrementar o conhecimento sobre os impactes da energia eólica na vida selvagem e para compreender quais as medidas que podem ser tomadas para os reduzir e, assim, garantir um futuro mais verde e sustentável para todas as formas de vida.
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Wan, Chung-him, and 溫仲謙. "Analysis of zero-inflated count data." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B43703719.
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Wan, Chung-him. "Analysis of zero-inflated count data." Click to view the E-thesis via HKUTO, 2009. http://sunzi.lib.hku.hk/hkuto/record/B43703719.
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Roemmele, Eric S. "A Flexible Zero-Inflated Poisson Regression Model." UKnowledge, 2019. https://uknowledge.uky.edu/statistics_etds/38.
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A practical problem often encountered with observed count data is the presence of excess zeros. Zero-inflation in count data can easily be handled by zero-inflated models, which is a two-component mixture of a point mass at zero and a discrete distribution for the count data. In the presence of predictors, zero-inflated Poisson (ZIP) regression models are, perhaps, the most commonly used. However, the fully parametric ZIP regression model could sometimes be restrictive, especially with respect to the mixing proportions. Taking inspiration from some of the recent literature on semiparametric mixtures of regressions models for flexible mixture modeling, we propose a semiparametric ZIP regression model. We present an "EM-like" algorithm for estimation and a summary of asymptotic properties of the estimators. The proposed semiparametric models are then applied to a data set involving clandestine methamphetamine laboratories and Alzheimer's disease.
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Jansakul, Naratip. "Some aspects of modelling overdispersed and zero-inflated count data." Thesis, University of Exeter, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.364435.
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Thomas, Gustavo. "GAMLSSs with applications to zero inflated and hierarquical data." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/11/11134/tde-06042018-150012/.
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The generalized additive models for location, scale and shape (GAMLSS) developed by Rigby and Stasinopoulos (2005) are a general class of univariate regression models that do not have the response distribution restricted to the exponential family as do the generalized linear and additive models, for example. In addition, they allow all the parameters of the response variable distribution to be modeled explicitly through different sets of explanatory variables. The semiparametric subclass of GAMLSS, in particular, accepts a wide range of parametric and nonparametric terms to be included in the predictors of the parameters. Similar to the generalized linear models, the GAMLSSs link predictors to parameters through monotonic link functions, which can also change for each parameter. This dissertation describes the GAMLSSs methodology and presents two applications to data sets provenient from experiments in agronomy; exploring methods of estimation, diagnosis and comparison of these models.Os modelos lineares generalizados para locação, escala e forma (GAMLSS) desenvolvidos por Rigby e Stasinopoulos (2005) são uma ampla classe de modelos de regressão univariados que não pressupõem que a distribuição da variável resposta pertença à família exponencial como os modelos lineares generalizados ou aditivos generalizados, por exemplo. Além do mais, eles permitem que todos os parâmetros da distribuição da variável resposta sejam modelados explicitamente por meio de diferentes conjuntos de variáveis explanatórias. A subclasse semiparamétrica dos GAMLSS, em particular, permite que uma grande variedade de termos paramétricos e não paramétricos sejam incluídos nos preditores dos parâmetros da distribuição assumida para a variável resposta. De forma análoga aos modelos lineares generalizados, os GAMLSSs ligam os preditores aos parâmetros por meio de funções de ligação monótonas, que também podem mudar de acordo com o parâmetro a ser estimado. Esta dissertação descreve a metodologia dos modelos lineares generalizados para locação, escala e forma e apresenta duas aplicações a bancos de dados provenientes de experimentos agrícolas; explorando métodos de estimação, diagnóstico e comparação desse tipo de modelos.
8
Bhaktha, Nivedita. "Properties of Hurdle Negative Binomial Models for Zero-Inflated and Overdispersed Count data." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1543573678017356.
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Zeileis, Achim, Christian Kleiber, and Simon Jackman. "Regression Models for Count Data in R." Foundation for Open Access Statistics, 2008. http://epub.wu.ac.at/4986/1/Zeileis_etal_2008_JSS_Regression%2DModels%2Dfor%2DCount%2DData%2Din%2DR.pdf.
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The classical Poisson, geometric and negative binomial regression models for count data belong to the family of generalized linear models and are available at the core of the statistics toolbox in the R system for statistical computing. After reviewing the conceptual and computational features of these methods, a new implementation of hurdle and zero-inflated regression models in the functions hurdle() and zeroinfl() from the package pscl is introduced. It re-uses design and functionality of the basic R functions just as the underlying conceptual tools extend the classical models. Both hurdle and zero-inflated model, are able to incorporate over-dispersion and excess zeros-two problems that typically occur in count data sets in economics and the social sciences-better than their classical counterparts. Using cross-section data on the demand for medical care, it is illustrated how the classical as well as the zero-augmented models can be fitted, inspected and tested in practice. (authors' abstract)
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Nian, Gaowei. "A score test of homogeneity in generalized additive models for zero-inflated count data." Kansas State University, 2014. http://hdl.handle.net/2097/18230.
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Master of ScienceDepartment of Statistics
Wei-Wen Hsu
Zero-Inflated Poisson (ZIP) models are often used to analyze the count data with excess zeros. In the ZIP model, the Poisson mean and the mixing weight are often assumed to depend on covariates through regression technique. In other words, the effect of covariates on Poisson mean or the mixing weight is specified using a proper link function coupled with a linear predictor which is simply a linear combination of unknown regression coefficients and covariates. However, in practice, this predictor may not be linear in regression parameters but curvilinear or nonlinear. Under such situation, a more general and flexible approach should be considered. One popular method in the literature is Zero-Inflated Generalized Additive Models (ZIGAM) which extends the zero-inflated models to incorporate the use of Generalized Additive Models (GAM). These models can accommodate the nonlinear predictor in the link function. For ZIGAM, it is also of interest to conduct inferences for the mixing weight, particularly evaluating whether the mixing weight equals to zero. Many methodologies have been proposed to examine this question, but all of them are developed under classical zero-inflated models rather than ZIGAM. In this report, we propose a generalized score test to evaluate whether the mixing weight is equal to zero under the framework of ZIGAM with Poisson model. Technically, the proposed score test is developed based on a novel transformation for the mixing weight coupled with proportional constraints on ZIGAM, where it assumes that the smooth components of covariates in both the Poisson mean and the mixing weight have proportional relationships. An intensive simulation study indicates that the proposed score test outperforms the other existing tests when the mixing weight and the Poisson mean truly involve a nonlinear predictor. The recreational fisheries data from the Marine Recreational Information Program (MRIP) survey conducted by National Oceanic and Atmospheric Administration (NOAA) are used to illustrate the proposed methodology.
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Fan, Huihao. "Test of Treatment Effect with Zero-Inflated Over-Dispersed Count Data from Randomized Single Factor Experiments." University of Cincinnati / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1407404513.
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Yang, Hui. "Adjusting for Bounding and Time-in-Sample Eects in the National Crime Victimization Survey (NCVS) Property Crime Rate Estimation." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1452167047.
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Kreider, Scott Edwin Douglas. "A case study in handling over-dispersion in nematode count data." Manhattan, Kan. : Kansas State University, 2010. http://hdl.handle.net/2097/4248.
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Zeileis, Achim, Christian Kleiber, and Simon Jackman. "Regression Models for Count Data in R." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 2007. http://epub.wu.ac.at/1168/1/document.pdf.
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The classical Poisson, geometric and negative binomial regression models for count data belong to the family of generalized linear models and are available at the core of the statistics toolbox in the R system for statistical computing. After reviewing the conceptual and computational features of these methods, a new implementation of zero-inflated and hurdle regression models in the functions zeroinfl() and hurdle() from the package pscl is introduced. It re-uses design and functionality of the basic R functions just as the underlying conceptual tools extend the classical models. Both model classes are able to incorporate over-dispersion and excess zeros - two problems that typically occur in count data sets in economics and the social and political sciences - better than their classical counterparts. Using cross-section data on the demand for medical care, it is illustrated how the classical as well as the zero-augmented models can be fitted, inspected and tested in practice. (author's abstract)Series: Research Report Series / Department of Statistics and Mathematics
15
Dartnall, James Edward. "Examining the effect of daylight on road accidents and investigating a state space time series approach to modelling zero inflated count data." Thesis, University of Southampton, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.438672.
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Llorens, Aleixandre Noelia. "Evaluación en el modelado de las respuestas de recuento." Doctoral thesis, Universitat de les Illes Balears, 2005. http://hdl.handle.net/10803/9446.
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Este trabajo presenta dos líneas de investigación desarrolladas en los últimos años en torno a la etapa de evaluación en datos de recuento. Los campos de estudio han sido: los datos de recuento, concretamente el estudio del modelo de regresión de Poisson y sus extensiones y la etapa de evaluación como punto de inflexión en el proceso de modelado estadístico. Los resultados obtenidos ponen de manifiesto la importancia de aplicar el modelo adecuado a las características de los datos así como de evaluar el ajuste del mismo. Por otra parte la comparación de pruebas, índices, estimadores y modelos intentan señalar la adecuación o la preferencia de unos sobre otros en determinadas circunstancias y en función de los objetivos del investigador.This paper presents two lines of research that have been developed in recent years on the evaluation stage in count data. The areas of study have been both count data, specifically the study of Poisson regression modelling and its extension, and the evaluation stage as a point of reflection in the statistical modelling process. The results obtained demonstrate the importance of applying appropriate models to the characteristics of data as well as evaluating their fit. On the other hand, comparisons of trials, indices, estimators and models attempt to indicate the suitability or preference for one over the others in certain circumstances and according to research objectives.
17
Garden, Cheryl Ellen. "Modeling zero inflated count data." Thesis, 1996. http://hdl.handle.net/2429/4495.
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A natural approach to analyzing the effect of covariates on a count response variable is to
use a Poisson regression model. A complication is that the counts are often more variable than
can be explained by a Poisson model. This problem, referred to as overdispersion, has received a
great deal of attention in recent literature and a number of variations on the Poisson regression
model have been developed. As such, statistical consultants are faced with the difficult task of
identifying which of these alternative models is best suited to their particular application. In this
thesis, two applications where the data exhibit overdispersion are investigated. In the first
application, two treatments for chronic urinary tract infections are compared. The response
variable represents the number of resistant strains of bacteria cultured from rectal swabs. In the
second application, the number of units sold of a product are modeled as depending on two
factors representing the day of the week and the store.
Two alternative models that allow for overdispersion are used in both applications. The
negative binomial regression model and the zero inflated Poisson regression model so named by
Lambert (Lambert, 1992) provide improved fits. Further, the zero inflated Poisson regression
model performs particularly well in the situation when the overdispersion is suspected to be due
to a large number of zeroes occurring in the data. The zero inflated Poisson regression model
allows one to both fit the data well and make some inference regarding the nature of the
overdispersion present. This little known model may prove to be valuable as there exist a
number of applications where observed overdispersion in a count response variable is clearly due
to an inflated number of zeroes.
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Hsu, Yu-Ling, and 許祐領. "Robust Inference for variance function of zero-inflated count responses." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/74970922220732267341.
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碩士國立中央大學
統計研究所
100
(一) zero-inflated and over-dispersed count data are encountered in many research areas. Such data are generally more difficult to analyze due to the scarcity of appropriate statistic models. We demonstrate that the normal model can be easily modified to provide asymptotically legitimate likelihood inference about the parameters for in the variance function . Contrast is also made with models proposed in the literatures.
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Ghanney, Bartholomew Embir. "Estimation of zero-inflated count time series models with and without covariates." 2015. http://hdl.handle.net/1993/30920.
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Zero inflation occurs when the proportion of zeros of a model is greater than the proportion of zeros of the corresponding Poisson model. This situation is very common in count data. In order to model zero inflated count time series data, we propose the zero inflated autoregressive conditional Poisson (ZIACP) model by the extending the autoregressive conditional poisson (ACP) model of Ghahramani and Thavaneswaran (2009). The stationarity conditions and the autocorrelation functions of the ZIACP model are provided. Based on the expectation maximization (EM) algorithm an estimation method is developed. A simulation study shows that the estimation method is accurate and reliable as long as the sample size is reasonably high. Three real data examples, syphilis data Yang (2012), arson data Zhu (2012) and polio data Kitromilidou and Fokianos (2015) are studied to compare the performance of the proposed model with other competitive models in the literature.February 2016
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Wang, Lijuan. "Generalized mixed models with mixture links for multivariate zero-inflated count data." 2008. http://wwwlib.umi.com/dissertations/fullcit/3362903.
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Mawella, Nadeesha R. "A robust test of homogeneity in zero-inflated models for count data." Diss., 2018. http://hdl.handle.net/2097/38877.
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Doctor of PhilosophyDepartment of Statistics
Wei-Wen Hsu
Evaluating heterogeneity in the class of zero-inflated models has attracted considerable attention in the literature, where the heterogeneity refers to the instances of zero counts generated from two different sources. The mixture probability or the so-called mixing weight in the zero-inflated model is used to measure the extent of such heterogeneity in the population. Typically, the homogeneity tests are employed to examine the mixing weight at zero. Various testing procedures for homogeneity in zero-inflated models, such as score test and Wald test, have been well discussed and established in the literature. However, it is well known that these classical tests require the correct model specification in order to provide valid statistical inferences. In practice, the testing procedure could be performed under model misspecification, which could result in biased and invalid inferences. There are two common misspecifications in zero-inflated models, which are the incorrect specification of the baseline distribution and the misspecified mean function of the baseline distribution. As an empirical evidence, intensive simulation studies revealed that the empirical sizes of the homogeneity tests for zero-inflated models might behave extremely liberal and unstable under these misspecifications for both cross-sectional and correlated count data. We propose a robust score statistic to evaluate heterogeneity in cross-sectional zero-inflated data. Technically, the test is developed based on the Poisson-Gamma mixture model which provides a more general framework to incorporate various baseline distributions without specifying their associated mean function. The testing procedure is further extended to correlated count data. We develop a robust Wald test statistic for correlated count data with the use of working independence model assumption coupled with a sandwich estimator to adjust for any misspecification of the covariance structure in the data. The empirical performances of the proposed robust score test and Wald test are evaluated in simulation studies. It is worth to mention that the proposed Wald test can be implemented easily with minimal programming efforts in a routine statistical software such as SAS. Dental caries data from the Detroit Dental Health Project (DDHP) and Girl Scout data from Scouting Nutrition and Activity Program (SNAP) are used to illustrate the proposed methodologies.
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Mamun, Md Abdullah Al. "Zero-inflated regression models for count data : an application to under-5 deaths." 2014. http://liblink.bsu.edu/uhtbin/catkey/1747408.
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Zero-inflated (ZI) count data models overcome the restriction of equality relationship between
mean and variance, but functional relationship still exists. For ZI models it is important to
know whether the proportion of zeros and the rate of counts have any influence on the fit of
the model. In this study we have considered three zero-inflated models, namely, ZIP, ZINB,
and Hurdle model. We also considered Poisson and negative binomial model as classical
count data models. Our simulation experiment suggests that the proportion of zeros for
given rate parameter does not a↵ect the fit of the models as long as model is correctly
specified. In case of misspecification of the model, it does not perform well for large rate
parameter. These three zero-inflated models performed better than the classical models as
the rate parameter and the proportion of zeros become larger. We applied five models to
the BDHS 2011 survey data to understand the social determinants associated with a mother
to experience under-5 deaths of her children. The classical models failed to di↵erentiate
between mothers who have experienced under-5 deaths of their children and who have never
experienced under-5 deaths. While zero-inflated models were able to di↵erentiate between
those two groups of mothers in terms of zero counts and positive counts of number of under-5
deaths of their children with associated covariates in opposite slope of coefficients. Among
the three zero-inflated models, Hurdle model performed best in fitting the data compared to
the ZIP and ZINB models.
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Sung, Chin-Hsiung, and 宋志雄. "Evaluation of Parameter Estimations in Log-Linear Model under Zero-Inflated Count Data." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/46545339679568069406.
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碩士國立臺北大學
統計學系
103
More and more customers use credit cards or electronic purse to pay their bills instead of real money. Quite frequently, people have more than one credit card on average. Nevertheless, only a few credit cards are used. To analyze the consumer behavior in using credit cards, there exists many zeros. Such a data with many zeros are called zero-inflated count data. To deal with the excess zeros, Lambert (1992) proposed a zero-inflated Poisson distribution. The most popular model for consumer consumption behavior was proposed by Ehrenberg (1959) which is called the plain vanilla model. To take into account of excess zeros, Wu (2008) combined Beta distribution and the plain vanilla model and proposed a beta-binomial model. Based on the derivation in Wu (2008), this thesis proposes combining Beta distribution with logistic model to deal with excess zeros. To understand the sensitivity of the distributional assumption, Monte Carlo simulation is conducted. Under various settings, the absolute bias and the prediction error are used to evaluate the performance of the estimators. A real data is used to illustrate the feasibility of the proposed model.
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Rodrigues-Motta, Mariana. "Zero-inflated poisson models for quantitative genetic analysis of count data with applications to mastitis in dairy cows." 2006. http://www.library.wisc.edu/databases/connect/dissertations.html.
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Bhattacharya, Archan. "Inference for controlled branching process, Bayesian inference for zero-inflated count data and Bayesian techniques for hairline fracture detection and reconstruction." 2007. http://purl.galileo.usg.edu/uga%5Fetd/bhattacharya%5Farchan%5F200705%5Fphd.
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Yu, Kuan Yi, and 余冠毅. "Some discussions on the performance of parameter estimations of the log-linear model and its extended models under the zero-inflated count data." Thesis, 2015. http://ndltd.ncl.edu.tw/handle/72534318388068624846.
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碩士國立臺北大學
統計學系
103
The most common parametric assumption for analyzing count data is Poisson distribution. However, it constructs under the assumption that the data have features that the mean equals variance. Nowadays, owing to there rapid development in technology storage, data are abundant and come from many different sources. In turn, the data no longer have the feature that the mean equals variance. Adding a new dispersion parameter in Poisson distribution, Consul and Jain (1970) proposed the generalized Poisson distribution. Mullahy (1986) suggested combining the Bernoulli and Poisson distribution to take into account the excess zeros in the data, which is called the zero-inflated Poisson distribution. The generalized linear model is often used to model the association between count data and potential covariates. The model is often constructed under Poisson distribution and log link assumption. However, the assumption of having the same mean and variance is violated, the Poisson assumption is relaxed to the Generalized Poisson or zip-inflated Poisson. Since Poisson distribution is relatively simple and easy to make statistical inference, the purpose of this thesis is then to evaluate the sensitivity of the distribution assumption on different data types using Monte Carlo simulations. 4 different types of data along with many simulation settings are generated. The parameter estimators of the generalized linear model under 4 different distribution assumptions are obtained. The sensitivity is assessed through the bias of the estimates and the mean square error.
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Rivest, Amélie. "La régression de Poisson multiniveau généralisée au sein d’un devis longitudinal : un exemple de modélisation du nombre d’arrestations de membres de gangs de rue à Montréal entre 2005 et 2007." Thèse, 2012. http://hdl.handle.net/1866/9924.
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Les données comptées (count data) possèdent des distributions ayant des caractéristiques particulières comme la non-normalité, l’hétérogénéité des variances ainsi qu’un nombre important de zéros. Il est donc nécessaire d’utiliser les modèles appropriés afin d’obtenir des résultats non biaisés. Ce mémoire compare quatre modèles d’analyse pouvant être utilisés pour les données comptées : le modèle de Poisson, le modèle binomial négatif, le modèle de Poisson avec inflation du zéro et le modèle binomial négatif avec inflation du zéro. À des fins de comparaisons, la prédiction de la proportion du zéro, la confirmation ou l’infirmation des différentes hypothèses ainsi que la prédiction des moyennes furent utilisées afin de déterminer l’adéquation des différents modèles. Pour ce faire, le nombre d’arrestations des membres de gangs de rue sur le territoire de Montréal fut utilisé pour la période de 2005 à 2007. L’échantillon est composé de 470 hommes, âgés de 18 à 59 ans. Au terme des analyses, le modèle le plus adéquat est le modèle binomial négatif puisque celui-ci produit des résultats significatifs, s’adapte bien aux données observées et produit une proportion de zéro très similaire à celle observée.Count data have distributions with specific characteristics such as non-normality, heterogeneity of variances and a large number of zeros. It is necessary to use appropriate models to obtain unbiased results. This memoir compares four models of analysis that can be used for count data: the Poisson model, the negative binomial model, the Poisson model with zero inflation and the negative binomial model with zero inflation. For purposes of comparison, the prediction of the proportion of zero, the confirmation or refutation of the various assumptions and the prediction of average number of arrrests were used to determine the adequacy of the different models. To do this, the number of arrests of members of street gangs in the Montreal area was used for the period 2005 to 2007. The sample consisted of 470 men, aged 18 to 59 years. After the analysis, the most suitable model is the negative binomial model since it produced significant results, adapts well to the observed data and produces a zero proportion very similar to that observed.