Control charts for individual observations of a bivariate Poisson process

In this paper, three single-control charts are proposed to monitor individual observations of a bivariate Poisson process. The specified false-alarm risk, their control limits, and ARLs were determined to compare their performances for different types and sizes of shifts. In most of the cases, the single charts presented better performance rather than two separate control charts ( one for each quality characteristic). A numerical example illustrates the proposed control charts.

A priori ratemaking using bivariate poisson regression models

In automobile insurance, it is useful to achieve a priori ratemaking by resorting to gene- ralized linear models, and here the Poisson regression model constitutes the most widely accepted basis. However, insurance companies distinguish between claims with or without bodily injuries, or claims with full or partial liability of the insured driver. This paper exa- mines an a priori ratemaking procedure when including two di®erent types of claim. When assuming independence between claim types, the premium can be obtained by summing the premiums for each type of guarantee and is dependent on the rating factors chosen. If the independence assumption is relaxed, then it is unclear as to how the tari® system might be a®ected. In order to answer this question, bivariate Poisson regression models, suitable for paired count data exhibiting correlation, are introduced. It is shown that the usual independence assumption is unrealistic here. These models are applied to an automobile insurance claims database containing 80,994 contracts belonging to a Spanish insurance company. Finally, the consequences for pure and loaded premiums when the independence assumption is relaxed by using a bivariate Poisson regression model are analysed.

Mixture of bivariate Poisson regression models with an application to insurance

In a recent paper Bermúdez [2009] used bivariate Poisson regression models for ratemaking in car insurance, and included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. In the present paper, we revisit this model in order to consider alternatives. We propose a 2-finite mixture of bivariate Poisson regression models to demonstrate that the overdispersion in the data requires more structure if it is to be taken into account, and that a simple zero-inflated bivariate Poisson model does not suffice. At the same time, we show that a finite mixture of bivariate Poisson regression models embraces zero-inflated bivariate Poisson regression models as a special case. Additionally, we describe a model in which the mixing proportions are dependent on covariates when modelling the way in which each individual belongs to a separate cluster. Finally, an EM algorithm is provided in order to ensure the models’ ease-of-fit. These models are applied to the same automobile insurance claims data set as used in Bermúdez [2009] and it is shown that the modelling of the data set can be improved considerably.

Control charts for individual observations of a bivariate Poisson process

In this paper, three single-control charts are proposed to monitor individual observations of a bivariate Poisson process. The specified false-alarm risk, their control limits, and ARLs were determined to compare their performances for different types and sizes of shifts. In most of the cases, the single charts presented better performance rather than two separate control charts ( one for each quality characteristic). A numerical example illustrates the proposed control charts.

Dependence Structure of some Bivariate Distributions

Dependence in the world of uncertainty is a complex concept. However, it exists, is asymmetric, has magnitude and direction, and can be measured. We use some measures of dependence between random events to illustrate how to apply it in the study of dependence between non-numeric bivariate variables and numeric random variables. Graphics show what is the inner dependence structure in the Clayton Archimedean copula and the Bivariate Poisson distribution. We know this approach is valid for studying the local dependence structure for any pair of random variables determined by its empirical or theoretical distribution. And it can be used also to simulate dependent events and dependent r/v/’s, but some restrictions apply. ACM Computing Classification System (1998): G.3, J.2.

Beta-binomial/Poisson regression models for repeated bivariate counts

We analyze data obtained from a study designed to evaluate training effects on the performance of certain motor activities of Parkinson`s disease patients. Maximum likelihood methods were used to fit beta-binomial/Poisson regression models tailored to evaluate the effects of training on the numbers of attempted and successful specified manual movements in 1 min periods, controlling for disease stage and use of the preferred hand. We extend models previously considered by other authors in univariate settings to account for the repeated measures nature of the data. The results suggest that the expected number of attempts and successes increase with training, except for patients with advanced stages of the disease using the non-preferred hand. Copyright (c) 2008 John Wiley & Sons, Ltd.

A class of bivariate Erlang distributions and ruin probabilities in multivariate risk models

Nous y introduisons une nouvelle classe de distributions bivariées de type Marshall-Olkin, la distribution Erlang bivariée. La transformée de Laplace, les moments et les densités conditionnelles y sont obtenus. Les applications potentielles en assurance-vie et en finance sont prises en considération. Les estimateurs du maximum de vraisemblance des paramètres sont calculés par l'algorithme Espérance-Maximisation. Ensuite, notre projet de recherche est consacré à l'étude des processus de risque multivariés, qui peuvent être utiles dans l'étude des problèmes de la ruine des compagnies d'assurance avec des classes dépendantes. Nous appliquons les résultats de la théorie des processus de Markov déterministes par morceaux afin d'obtenir les martingales exponentielles, nécessaires pour établir des bornes supérieures calculables pour la probabilité de ruine, dont les expressions sont intraitables.

Dynamic fator Models for bivariate Count Data: an application to fire activity

The study of forest re activity, in its several aspects, is essencial to understand the phenomenon and to prevent environmental public catastrophes. In this context the analysis of monthly number of res along several years is one aspect to have into account in order to better comprehend this tematic. The goal of this work is to analyze the monthly number of forest res in the neighboring districts of Aveiro and Coimbra, Portugal, through dynamic factor models for bivariate count series. We use a bayesian approach, through MCMC methods, to estimate the model parameters as well as to estimate the common latent factor to both series.

Variables Associated With The Performance Of Centers For Dental Specialties In Brazil.

The aim of this study was to evaluate the performance of the Centers for Dental Specialties (CDS) in the country and associations with sociodemographic indicators of the municipalities, structural variables of services and primary health care organization in the years 2004-2009. The study used secondary data from procedures performed in the CDS to the specialties of periodontics, endodontics, surgery and primary care. Bivariate analysis by χ2 test was used to test the association between the dependent variable (performance of the CDS) with the independents. Then, Poisson regression analysis was performed. With regard to the overall achievement of targets, it was observed that the majority of CDS (69.25%) performance was considered poor/regular. The independent factors associated with poor/regular performance of CDS were: municipalities belonging to the Northeast, South and Southeast regions, with lower Human Development Index (HDI), lower population density, and reduced time to deployment. HDI and population density are important for the performance of the CDS in Brazil. Similarly, the peculiarities related to less populated areas as well as regional location and time of service implementation CDS should be taken into account in the planning of these services.

Dyspareunia In Hiv-positive And Hiv-negative Middle-aged Women: A Cross-sectional Study.

To evaluate whether dyspareunia is associated with HIV status in menopausal women and also to assess which factors are associated with dyspareunia in a group of HIV-positive menopausal women. A cross-sectional study was conducted with 178 HIV-negative and 128 HIV-positive women aged 40-60 years. The Short Personal Experiences Questionnaire (SPEQ) was used to collect data. Sociodemographic, clinical, behavioural and reproductive factors were evaluated, as well as factors related to the HIV infection. Dyspareunia was defined as pain during intercourse. A bivariate analysis and Poisson multiple regression analysis were performed. Overall, 41.4% of the HIV-positive women reported dyspareunia compared with 34.8% of the HIV-negative women (p=0.242). In the HIV-positive women, bivariate analysis revealed an association between dyspareunia and having a steady partner (p=0.047); the woman's partner having undergone HIV testing (p=0.020); vaginal dryness (p<0.001); muscle/joint pain (p=0.021); physical/emotional violence (p=0.049); urinary incontinence (p=0.004); and the use of lamivudine/zidovudine (p=0.048). The Poisson multiple regression analysis found an association between dyspareunia and vaginal dryness (prevalence ratio (PR)=1.96, 95% CI 1.10 to 3.50, p=0.023) and urinary incontinence (PR=1.86, 95% CI 1.06 to 3.27, p=0.031). Dyspareunia was common in this group of HIV-positive women and was associated principally with vaginal dryness and urinary incontinence. The importance of treating dyspareunia within the context of sexual health in this group of women should be emphasised and appropriate management of this issue may reduce the likelihood of lesions on the vaginal wall, which may act as a portal of entry for other infections.

[need For Orthodontic Treatment Among Brazilian Adolescents: Evaluation Based On Public Health].

To identify the prevalence and the severity of malocclusions and to analyze factors associated with the need for orthodontic treatment of Brazilian adolescents. This exploratory, cross-sectional study was carried out based on secondary data from the national epidemiological survey on oral health in Brazil (2002-2003). Socio-demographic conditions, self-perception, and the existence and degree of malocclusion, using the Dental Aesthetic Index, were evaluated in 16,833 adolescent Brazilians selected by probabilistic sample by conglomerates. The dependent variable - need orthodontic treatment - was estimated from the severity of malocclusion. The magnitude and direction of the association in bivariate and multivariate analyzes from a Robust Poisson regression was estimated RESULTS: The majority of the adolescents needed orthodontic treatment (53.2%). In the multivariate analysis, the prevalence of the need for orthodontic treatment was larger among females, non-whites, those that perceived a need for treatment, and those that perceived their appearance as normal, bad, or very bad. The need for orthodontic treatment was smaller among those that lived in the Northeast and Central West macro-regions compared to those living in Southeast Brazil and it was also smaller among those that perceived their chewing to be normal or their oral health to be bad or very bad. There was a high prevalence of orthodontic treatment need among adolescents in Brazil and this need was associated with demographic and subjective issues. The high prevalence of orthodontic needs in adolescents is a challenge to the goals of Brazil's universal public health system.

Consumo abusivo e dependência de álcool em população adulta no Estado de São Paulo, Brasil

OBJETIVO: Descrever as prevalências de consumo abusivo e dependência de álcool em população adulta de 20 a 59 anos no Estado de São Paulo, e suas associações com variáveis demográficas e socioeconômicas. MÉTODOS: Inquérito domiciliar do tipo transversal (ISA-SP), em quatro áreas do Estado de São Paulo: a) Região Sudoeste da Grande São Paulo, constituída pelos Municípios de Taboão da Serra, Itapecerica da Serra e Embu; b) Distrito do Butantã, no Município de São Paulo; c) Município de Campinas e; d) Município de Botucatu. Foi considerado consumo abusivo de álcool a ingestão em dia típico de 30 gramas ou mais de etanol para os homens, e 24 gramas ou mais para as mulheres. A dependência de álcool foi caracterizada pelo questionário CAGE. Análises bivariadas e multivariadas dos dados foram realizadas a partir de Modelos de Regressão de Poisson. Todas as análises foram estratificadas por sexo. RESULTADOS: Em 1.646 adultos entrevistados, a prevalência de consumo abusivo de álcool foi de 52,9% no sexo masculino e 26,8% no sexo feminino. Quanto à dependência de álcool, foram observadas duas ou mais respostas positivas no teste CAGE em 14,8% dos homens e em 5,4% das mulheres que relataram consumir álcool. Isto corresponde a uma prevalência populacional de dependência de 10,4% nos homens e 2,6% nas mulheres. O consumo abusivo de álcool no sexo masculino apresentou associação inversa à faixa etária e associação direta à escolaridade e ao tabagismo. No sexo feminino, observou-se associação direta do consumo abusivo de álcool com a escolaridade e o tabagismo, e com as situações conjugais sem companheiro. A dependência de álcool no sexo masculino associou-se a não exercer atividade de trabalho e à baixa escolaridade. No sexo feminino não houve associação do CAGE com nenhuma das variáveis estudadas. CONCLUSÕES: Pela alta prevalência de consumidores e dependentes, é essencial a identificação dos segmentos sociodemográficos mais vulneráveis ao consumo abusivo e dependência de álcool. As associações entre a dependência/abuso e não estar exercendo atividade de trabalho, no sexo masculino, e a maior prevalência em mulheres de escolaridade universitária, sugerem componentes para programas de intervenção e controle.

Additive genetic relationship of longevity with fertility and production traits in Nellore cattle based on bivariate models

Survival or longevity is an economically important trait in beef cattle. The main inconvenience for its inclusion in selection criteria is delayed recording of phenotypic data and the high computational demand for including survival in proportional hazard models. Thus, identification of a longevity-correlated trait that could be recorded early in life would be very useful for selection purposes. We estimated the genetic relationship of survival with productive and reproductive traits in Nellore cattle, including weaning weight (WW), post-weaning growth (PWG), muscularity (MUSC), scrotal circumference at 18 months (SC18), and heifer pregnancy (HP). Survival was measured in discrete time intervals and modeled through a sequential threshold model. Five independent bivariate Bayesian analyses were performed, accounting for cow survival and the five productive and reproductive traits. Posterior mean estimates for heritability (standard deviation in parentheses) were 0.55 (0.01) for WW, 0.25 (0.01) for PWG, 0.23 (0.01) for MUSC, and 0.48 (0.01) for SC18. The posterior mean estimates (95% confidence interval in parentheses) for the genetic correlation with survival were 0.16 (0.13-0.19), 0.30 (0.25-0.34), 0.31 (0.25-0.36), 0.07 (0.02-0.12), and 0.82 (0.78-0.86) for WW, PWG, MUSC, SC18, and HP, respectively. Based on the high genetic correlation and heritability (0.54) posterior mean estimates for HP, the expected progeny difference for HP can be used to select bulls for longevity, as well as for post-weaning gain and muscle score.

The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set. (C) 2010 Elsevier B.V. All rights reserved.

POISSON DISTRIBUTION TO ANALYZE NEAR-THRESHOLD MOTOR EVOKED POTENTIALS

Motor unit action potentials (MUAPs) evoked by repetitive, low-intensity transcranial magnetic stimulation can be modeled as a Poisson process. A mathematical consequence of such a model is that the ratio of the variance to the mean of the amplitudes of motor evoked potentials (MEPs) should provide an estimate of the mean size of the individual MUAPs that summate to generate each MEP. We found that this is, in fact, the case. Our finding thus supports the use of the Poisson distribution to model MEP generation and indicates that this model enables characterization of the motor unit population that contributes to near-threshold MEPs. Muscle Nerve 42: 825-828, 2010