Multivariate count data are found in a variety of fields. For modeling such data, one may consider the multivariate Poisson distribution. Overdispersion is a problem when modeling the data with the multivariate Poisson distribution. Therefore, in this thesis we propose a new multivariate Poisson hidden Markov model based on the extension of independent multivariate Poisson finite mixture models, as a solution to this problem. This model, which can take into account the spatial nature of weed counts, is applied to weed species counts in an agricultural field. The distribution of counts depends on the underlying sequence of states, which are unobserved or hidden. These hidden states represent the regions where weed counts are relatively homogeneous. Analysis of these data involves the estimation of the number of hidden states, Poisson means and covariances. Parameter estimation is done using a modified EM algorithm for maximum likelihood estimation. <p>We extend the univariate Markov-dependent Poisson finite mixture model to the multivariate Poisson case (bivariate and trivariate) to model counts of two or three species. Also, we contribute to the hidden Markov model research area by developing Splus/R codes for the analysis of the multivariate Poisson hidden Markov model. Splus/R codes are written for the estimation of multivariate Poisson hidden Markov model using the EM algorithm and the forward-backward procedure and the bootstrap estimation of standard errors. The estimated parameters are used to calculate the goodness of fit measures of the models.<p>Results suggest that the multivariate Poisson hidden Markov model, with five states and an independent covariance structure, gives a reasonable fit to this dataset. Since this model deals with overdispersion and spatial information, it will help to get an insight about weed distribution for herbicide applications. This model may lead researchers to find other factors such as soil moisture, fertilizer level, etc., to determine the states, which govern the distribution of the weed counts.

In this thesis we investigate thinning of the renewal process. After multinomial thinning from a renewal process A, we obtain the k thinned processes, A_i , i =1,¡K, k. Based on some characterizations of the Poisson process as a renewal process, we give another characterizations of the Poisson process from some relations of expectation, variance, covariance, residual life of the k thinned processes. Secondly, we consider that at each arrival time we allow the number of arrivals to be i.i.d. random variables, also the mass of each unit atom can be split into k new atoms with the i-th new atom assigned to the process D_i , i =1,¡K, k. We also have characterizations of the Poisson process from some relations of expectation, variance of the process D_i , i =1,¡K, k.

We utilise several asset pricing models that allow for discontinuities in the returns and volatility time series in order to obtain estimates of Value-at-Risk (VaR). The first class of model that we use mixes a continuous diffusion process with discrete jumps at random points in time (Poisson Jump Diffusion Model). We also apply a purely discontinuous model that does not contain any continuous component at all in the underlying distribution (Variance Gamma Model). These models have been shown to have some success in capturing certain characteristics of return distributions, a few being leptokurtosis and skewness. Calibrating these models onto the returns of an index of Australian stocks (All Ordinaries Index), we then use the resulting parameters to obtain daily estimates of VaR. In order to obtain the VaR estimates for the Poisson Jump Diffusion Model and the Variance Gamma Model, we introduce the use of an innovation from option pricing techniques, which concentrates on the more tractable characteristic functions of the models. Having then obtained a series of VaR estimates, we then apply a variety of criteria to assess how each model performs and also evaluate these models against the traditional approaches to calculating VaR, such as that suggested by J.P. Morgan???s RiskMetrics. Our results show that whilst the Poisson Jump Diffusion model proved the most accurate at the 95% VaR level, neither the Poisson Jump Diffusion or Variance Gamma models were dominant in the other performance criteria examined. Overall, no model was clearly superior according to all the performance criteria analysed, and it seems that the extra computational time required to calibrate the Poisson Jump Diffusion and Variance Gamma models for the purposes of VaR estimation do not provide sufficient reward for the additional effort than that currently employed by Riskmetrics.

Thesis (M.Sc. (Hons.)) -- University of Western Sydney, 2001. / "A thesis presented to the University of Western Sydney in partial fulfilment of the requirements for the degree of Master of Science" Bibliography : leaves 65-69.

Thesis (M. Sc.)--Carleton University, 2008. / Includes bibliographical references (p. 57-62). Also available in electronic format on the Internet.

Thesis (Ph.D.)--Baylor University, 2008. / Includes bibliographical references (p. 99-101).

Thesis (M.S.)--Duquesne University, 2004. / Title from document title page. Abstract included in electronic submission form. Includes bibliographical references (p. 30).

Thesis (Ph.D.)--Baylor University, 2009. / Includes bibliographical references (p. 175-178).

Esta dissertação apresenta a modelagem e o monitoramento de características de qualidade do tipo taxa, que apresentam valores restritos ao intervalo [0,∞). A motivação inicial é que a característica de qualidade do tipo taxa pode ser modelada pela distribuição Poisson e, geralmente, a modelagem e o monitoramento não utilizam tal distribuição. Os objetivos desta dissertação são: (i) Propor uma nova carta de controle (CC), Carta Poisson, para monitorar características de qualidade do tipo taxa, com adaptação no cálculo dos limites de controle utilizando a distribuição Poisson; (ii) Propor uma CC baseada em modelo de regressão utilizando a distribuição de Poisson para monitorar características de qualidade do tipo taxa em função das variáveis de controle do processo e (iii) Propor índices de capacidade MRPOISSON Cp e MRPOISSON Cpk para avaliar processos monitorados por CCs baseadas em modelos de regressão utilizando a distribuição de Poisson. As cartas de controle e os índices de capacidade propostos foram avaliados aplicando exemplos retirados da literatura. As cartas de controle foram comparadas através do número médio de amostras (NMA) via simulação de Monte Carlo. Concluiu-se que as cartas de controle propostas são adequadas para a modelagem e o monitoramento de características de qualidade do tipo taxa pois detectaram mais rapidamente todas as alterações induzidas, apresentando melhor desempenho em comparação com outras cartas similares encontradas na literatura. / This paper presents the modeling and monitoring of quality features like rate, which have values restricted to the interval [0, ∞). The initial motivation is that the quality characteristic of the type rate can be modeled by the Poisson distribution, and generally, modeling and monitoring do not use such a distribution. The objectives of this dissertation are: (i) to propose a new control chart (CC), Poisson Charter, to monitor quality characteristics of the type rate, adapted to calculate the control limits using a Poisson distribution, (ii) propose a CC based on regression model using the Poisson distribution to monitor quality characteristics like rate as a function of the control variables of the process and (iii) Propose capability indices MRPOISSON Cp and MRPOISSON Cpk to evaluate processes and monitored by CCs based on regression models using the distribution of Poisson. The control charts and capability indices were estimated by applying the proposed examples from the literature. The control charts were compared using the average number of samples (NMA) via Monte Carlo simulation. It was concluded that the proposed control charts are suitable for modeling and monitoring of quality characteristics of the type detected faster rate because all the changes induced, showing better performance in comparison with other similar letters found in the literature.

Orientador: José Carlos Barbosa / Banca: Daniel Junior de Andrade / Banca: Francisco Jorge Cividanes / Banca: José Roberto Scarpellini / Banca: Marcelo Francisco Arantes Pereira / Resumo: O amendoim é cultivado em vários estados no Brasil sendo São Paulo o maior produtor, seguido da Bahia e Mato Grosso. Semeadas em épocas diferentes conforme a região do cultivo, a área cultivada do amendoim na safra de 2014/15 no Brasil abrangeu uma área de 107,4 mil hectares, com uma produção média de 3140 kg ha⁻¹. Duas pragas destacam-se pela importância nessa cultura, sendo a lagarta-do-pescoço-vermelho, Stegasta bosquella (Chambers, 1875) (Lepidoptera: Gelechiidae) e o tripes-do-prateamento, Enneothrips flavens Moulton, 1941 (Thysanoptera: Thripidae) por causarem elevados prejuízos econômicos ao agricultor. Na literatura, poucas informações são relatadas de amostragens de pragas no amendoinzeiro. Assim, associando-se esse fato a importância das duas pragas na cultura do amendoim, se fez necessário um estudo por meio de modelos probabilísticos para avaliar as suas distribuições espaciais e amostragens sequenciais, gerando assim futuras informações aos agricultores para o manejo integrado de pragas nessa cultura. Os experimentos foram conduzidos nos anos de 2013/2014 e 2014/2015, em Jaboticabal - SP, utilizando uma área de 1,08 ha, subdividida em 100 parcelas iguais de 108 m² (10,0 x 10,8 m). Em cada parcela foram avaliadas cinco plantas ao acaso, considerando a presença ou não de insetos de S. bosquella e E. flavens. Pelos dados, observaram-se uma distribuição agregada ou moderadamente agregada de E. flavens e uma distribuição aleatória de S. bosquella; o modelo de distribu... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The Peanuts are grown in several states in Brazil and São Paulo is the largest producer, followed by Bahia and Mato Grosso. Sown at different times as the growing region, the cultivated peanut area in 2014/15 crop in Brazil covered an area of 107,400 hectares, with an average production of 3140 kg ha⁻¹. Two pests stand out the importance that culture, and the red-necked peanut worm, Stegasta bosquella (Chambers, 1875) (Lepidoptera: Gelechiidae) and silvering thrips, Enneothrips flavens Moulton, 1941 (Thysanoptera: Thripidae) to cause high economic losses to the farmer. In the literature, little information is reported samplings pest in groundnut. Thus, associating this fact the importance of the two pests in peanut crop, a study using probabilistic models to assess their spatial and sequential sampling distributions made necessary, thus generating further information to farmers for the integrated pest management that culture. The experiments were conducted in the years 2013/2014 and 2014/2015, in Jaboticabal - SP, using an area of 1,08 ha, divided into 100 equal installments of 108 m² (10,0 x 10,8 m). In each plot were evaluated 5 randomly plants considering the presence or absence of E. flavens insects and S. bosquella. From the data, they observed an aggregate or aggregate distribution moderately E. flavens and a random distribution S. bosquella; the distribution model best fit for E. flavens was the negative binomial and larvae of S. bosquella the Poisson distribution model. These results allowed the development of sequential sampling plans in which, thrips and caterpillars have two lines: an upper (S1 = 6.3072 + 1.0680 N), (S1 = 3.2134 + 0.3274 N), the from which it is recommended to control; and bottom (S0 = -6.3072 + 1.0680 N) (S0 = -3.2134 + 0.3274 N), in which control is not recommended, respectively. The results ... (Complete abstract click electronic access below) / Doutor