The zero-inflated Conway-Maxwell-Poisson distribution: Bayesian inference, regression modeling and influence diagnostic

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The Conway-Maxwell-Poisson-generalized gamma regression model with long-term survivors

In this paper, we proposed a flexible cure rate survival model by assuming the number of competing causes of the event of interest following the Conway-Maxwell distribution and the time for the event to follow the generalized gamma distribution. This distribution can be used to model survival data when the hazard rate function is increasing, decreasing, bathtub and unimodal-shaped including some distributions commonly used in lifetime analysis as particular cases. Some appropriate matrices are derived in order to evaluate local influence on the estimates of the parameters by considering different perturbations, and some global influence measurements are also investigated. Finally, data set from the medical area is analysed.

The exponential COM-Poisson distribution

The Conway-Maxwell Poisson (COMP) distribution as an extension of the Poisson distribution is a popular model for analyzing counting data. For the first time, we introduce a new three parameter distribution, so-called the exponential-Conway-Maxwell Poisson (ECOMP) distribution, that contains as sub-models the exponential-geometric and exponential-Poisson distributions proposed by Adamidis and Loukas (Stat Probab Lett 39:35-42, 1998) and KuAY (Comput Stat Data Anal 51:4497-4509, 2007), respectively. The new density function can be expressed as a mixture of exponential density functions. Expansions for moments, moment generating function and some statistical measures are provided. The density function of the order statistics can also be expressed as a mixture of exponential densities. We derive two formulae for the moments of order statistics. The elements of the observed information matrix are provided. Two applications illustrate the usefulness of the new distribution to analyze positive data.

A Bayesian analysis of the Conway-Maxwell-Poisson cure rate model

The purpose of this paper is to develop a Bayesian analysis for the right-censored survival data when immune or cured individuals may be present in the population from which the data is taken. In our approach the number of competing causes of the event of interest follows the Conway-Maxwell-Poisson distribution which generalizes the Poisson distribution. Markov chain Monte Carlo (MCMC) methods are used to develop a Bayesian procedure for the proposed model. Also, some discussions on the model selection and an illustration with a real data set are considered.

Destructive weighted Poisson cure rate models

In this paper, we develop a flexible cure rate survival model by assuming the number of competing causes of the event of interest to follow a compound weighted Poisson distribution. This model is more flexible in terms of dispersion than the promotion time cure model. Moreover, it gives an interesting and realistic interpretation of the biological mechanism of the occurrence of event of interest as it includes a destructive process of the initial risk factors in a competitive scenario. In other words, what is recorded is only from the undamaged portion of the original number of risk factors.

COM-Poisson cure rate survival models and an application to a cutaneous melanoma data

In this paper, we develop a flexible cure rate survival model by assuming the number of competing causes of the event of interest to follow the Conway-Maxwell Poisson distribution. This model includes as special cases some of the well-known cure rate models discussed in the literature. Next, we discuss the maximum likelihood estimation of the parameters of this cure rate survival model. Finally, we illustrate the usefulness of this model by applying it to a real cutaneous melanoma data. (C) 2009 Elsevier B.V. All rights reserved.

A Bayesian destructive weighted Poisson cure rate model and an application to a cutaneous melanoma data

In this article, we propose a new Bayesian flexible cure rate survival model, which generalises the stochastic model of Klebanov et al. [Klebanov LB, Rachev ST and Yakovlev AY. A stochastic-model of radiation carcinogenesis - latent time distributions and their properties. Math Biosci 1993; 113: 51-75], and has much in common with the destructive model formulated by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)]. In our approach, the accumulated number of lesions or altered cells follows a compound weighted Poisson distribution. This model is more flexible than the promotion time cure model in terms of dispersion. Moreover, it possesses an interesting and realistic interpretation of the biological mechanism of the occurrence of the event of interest as it includes a destructive process of tumour cells after an initial treatment or the capacity of an individual exposed to irradiation to repair altered cells that results in cancer induction. In other words, what is recorded is only the damaged portion of the original number of altered cells not eliminated by the treatment or repaired by the repair system of an individual. Markov Chain Monte Carlo (MCMC) methods are then used to develop Bayesian inference for the proposed model. Also, some discussions on the model selection and an illustration with a cutaneous melanoma data set analysed by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)] are presented.

The Poisson-exponential distribution: a Bayesian approach

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Aplicación de colas de Poisson en procesos de ‘toma de decisiones’ en la gestión de servicios médicos

En este documento se revisa teóricamente la distribución de probabilidad de Poisson como función que asigna a cada suceso definido, sobre una variable aleatoria discreta, la probabilidad de ocurrencia en un intervalo de tiempo o región del espacio disjunto. Adicionalmente se revisa la distribución exponencial negativa empleada para modelar el intervalo de tiempo entre eventos consecutivos de Poisson que ocurren de manera independiente; es decir, en los cuales la probabilidad de ocurrencia de los eventos sucedidos en un intervalo de tiempo no depende de los ocurridos en otros intervalos de tiempo, por esta razón se afirma que es una distribución que no tiene memoria. El proceso de Poisson relaciona la función de Poisson, que representa un conjunto de eventos independientes sucedidos en un intervalo de tiempo o región del espacio con los tiempos dados entre la ocurrencia de los eventos según la distribución exponencial negativa. Los anteriores conceptos se usan en la teoría de colas, rama de la investigación de operaciones que describe y brinda soluciones a situaciones en las que un conjunto de individuos o elementos forman colas en espera de que se les preste un servicio, por lo cual se presentan ejemplos de aplicación en el ámbito médico.

A unified view on lifetime distributions arising from selection mechanisms

In this paper, we formulate a flexible density function from the selection mechanism viewpoint (see, for example, Bayarri and DeGroot (1992) and Arellano-Valle et al. (2006)) which possesses nice biological and physical interpretations. The new density function contains as special cases many models that have been proposed recently in the literature. In constructing this model, we assume that the number of competing causes of the event of interest has a general discrete distribution characterized by its probability generating function. This function has an important role in the selection procedure as well as in computing the conditional personal cure rate. Finally, we illustrate how various models can be deduced as special cases of the proposed model. (C) 2011 Elsevier B.V. All rights reserved.

Processus de Poisson généralisé autorégressif d'ordre 1

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Processus de Poisson généralisé autorégressif d'ordre 1

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Size-dependent predation by Dugesia lugubris (Turbellaria) on Physa acuta (Gastropoda): experiments and model

1. We investigated experimentally predation by the flatworm Dugesia lugubris on the snail Physa acuta in relation to predator body length and to prey morphology [shell length (SL) and aperture width (AW)]. 2. SL and AW correlate strongly in the field, but display significant and independent variance among populations. In the laboratory, predation by Dugesia resulted in large and significant selection differentials on both SL and AW. Analysis of partial effects suggests that selection on AW was indirect, and mediated through its strong correlation with SL. 3. The probability P(ij) for a snail of size category i (SL) to be preyed upon by a flatworm of size category j was fitted with a Poisson-probability distribution, the mean of which increased linearly with predator size (i). Despite the low number of parameters, the fit was excellent (r2 = 0.96). We offer brief biological interpretations of this relationship with reference to optimal foraging theory. 4. The largest size class of Dugesia (>2 cm) did not prey on snails larger than 7 mm shell length. This size threshold might offer Physa a refuge against flatworm predation and thereby allow coexistence in the field. 5. Our results are further discussed with respect to previous field and laboratory observations on P acuta life-history patterns, in particular its phenotypic variance in adult body size.

Nível de atividade física como estimador da aptidão física de estudantes universitários: explorando a adoção de questionário através de modelagem linear

A classificação do nível de atividade física (NAF) tem-se revelado aspecto controvertido em Ciência do Esporte. Nesta perspectiva, o objetivo da presente investigação foi verificar a utilização de instrumento adaptado para classificação do NAF. Para tanto, foi desenvolvido estudo transversal seriado, considerando NAF como variável independente e a aptidão física como dependente. Identificaram-se como população de estudo calouros do curso de Medicina, em total de 290 pessoas. Foram coletados durante três anos subseqüentes, através de anamnese dirigida, informações a respeito do NAF e testes de capacidade aeróbia e muscular, para conhecer as variáveis de aptidão física (AF). A análise estatística foi realizada através do modelo Linear, sendo aplicado o teste F para avaliar o efeito das variáveis independentes, bem como a prova de Tukey para comparar as respectivas médias e o modelo de Poisson para verificar o efeito das variáveis dependentes, segundo nível de atividade física e sexo. Como principal resultado, destaca-se o fato de as pessoas que referiram maior NAF também apresentaram os melhores escores de AF indicando que a utilização do instrumento revelou-se coerente e compatível.

Melhoria do planejamento para o fornecimento de materiais de modificações em aeronaves executivas

This paper presents a material demand forecasting to executive aircrafts modifications, the objective was to determinate a cadence of kits of materials in order reduce over stock, but also keeping the customer quality support. This work was motivated by the strong tendency that the market has to cut costs, especially those that do not add value to the product, waste. To solve the problem the Poisson probability distribution was used and also the error measures MPE, MAPE and MSE. At the end, after some adjustments, we found a satisfactory model for the problem