Self-Similarity and Lamperti Convergence for Families of Stochastic Processes

We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to a number of important families of processes that are not self-similar in the conventional sense. This includes a new class of fractional Hougaard motions defined as moving averages of Hougaard L\'evy process, as well as some well-known families of Hougaard L\'evy processes such as the Poisson processes, Brownian motions with drift, and the inverse Gaussian processes. Such families have many properties in common with ordinary self-similar processes, including the form of their covariance functions, and the fact that they appear as limits in a Lamperti-type limit theorem for families of stochastic processes.Comment: 23 pages. IMADA preprint 2010-09-0

Some discrete exponential dispersion models : poisson-tweedie and hinde-demétrio classes

In this paper we investigate two classes of exponential dispersion models (EDMs) for overdispersed count data with respect to the Poisson distribution. The first is a class of Poisson mixture with positive Tweedie mixing distributions. As an approximation (in terms of unit variance function) of the first, the second is a new class of EDMs characterized by their unit variance functions of the form µ + µp, where p is a real index related to a precise model. These two classes provide some alternatives to the negative binomial distribution (p = 2) which is classically used in the framework of regression models for count data when overdispersion results in a lack of fit of the Poisson regression model. Some properties are then studied and the practical usefulness is also discussed

Hierarchical models with normal and conjugate random effects : a review

Molenberghs, Verbeke, and Demétrio (2007) and Molenberghs et al. (2010) proposed a general framework to model hierarchical data subject to within-unit correlation and/or overdispersion. The framework extends classical overdispersion models as well as generalized linear mixed models. Subsequent work has examined various aspects that lead to the formulation of several extensions. A unified treatment of the model framework and key extensions is provided. Particular extensions discussed are: explicit calculation of correlation and other moment-based functions, joint modelling of several hierarchical sequences, versions with direct marginally interpretable parameters, zero-inflation in the count case, and influence diagnostics. The basic models and several extensions are illustrated using a set of key examples, one per data type (count, binary, multinomial, ordinal, and time-to-event)

Aplicação de alguns herbicidas na cultura da couve-flor (Brassica oleracea var. botrytis)

An experiment about herbicide use on cauliflower (Brassica oleracea var. botrytis) crop was conducted in the Experimental Field of Horticulture Section DAH-ESALQ, Piracicaba, Brazil. It was tested Dacthal (DCPA), Tenoran (chloroxuron), Afalon (linuron) and Ramrod (propachlor). Dacthal, Ramrod and Tenoran were not fitotoxic to cauliflower, and Afa-lon was very toxic. The herbicide that gave the best results to cauliflower was Ramrod.Foi conduzido na Área Experimental do Setor de Horticultura, DAH-ESALQ, Piracicaba, um experimento sobre o uso de alguns herbicidas na cultura da couve-flor (Brassica oleracea var. botrytis). Os herbicidas foram Dacthal (DCPA), Tenoran (cloroxuron), Afalon (linuron) e Ramrod (propacloro). O Dacthal, Ramrod, e o Tenoran não foram fitotóxicos à couve-flor, enquanto que o Afalon foi muito fitotóxico. O herbicida que melhor resultado apresentou para a couve-flor foi o Ramrod

Radiação solar disponível em Manaus (AM) e sua relação com a duração do brilho solar

Measurements of global solar radiation at ground level (Qg), were made at INPA, Manaus-AM, using a Eppley pyranometer during 1977 to 1979. The correlation between (Qg) and (QO) has the following relationship Qg = QO (0,26 + 0,49 n/N). Daily values of radiation and insolation for the study period are also presented. The mean daily radiation was 373 cal. cm-2 day-1 for this period.Medidas de radiação solar global, ao nível do solo (Og), foram realizadas na sede do INPA em Manaus-AM, com um piranômetro Eppley no período de 1977 a 1979. Foi estudada a correlação entre a radiação solar global e a insolação. O resultado obtido foi Og = Qo (0,26 + 0,49 n/N). São apresentados também os valores diários de radiação e de insolação. O valor médio diário de radiação solar encontrado para o período foi de 373 cal. cm-2 dia-1

Half-normal plots and overdispersed models in r: the hnp package

Count and proportion data may present overdispersion, i.e., greater variability than expected by the Poisson and binomial models, respectively. Different extended generalized linear models that allow for overdispersion may be used to analyze this type of data, such as models that use a generalized variance function, random-effects models, zero-inflated models and compound distribution models. Assessing goodness-of-fit and verifying assumptions of these models is not an easy task and the use of half-normal plots with a simulated envelope is a possible solution for this problem. These plots are a useful indicator of goodness-of-fit that may be used with any generalized linear model and extensions. For GLIM users, functions that generated these plots were widely used, however, in the open-source software R, these functions were not yet available on the Comprehensive R Archive Network (CRAN). We describe a new package in R, hnp, that may be used to generate the half-normal plot with a simulated envelope for residuals from different types of models. The function hnp ( ) can be used together with a range of different model fitting packages in R that extend the basic generalized linear model fitting in glm ( ) and is written so that it is relatively easy to extend it to new model classes and different diagnostics. We illustrate its use on a range of examples, including continuous and discrete responses, and show how it can be used to inform model selection and diagnose overdispersion

Models for overdispersed data in entomology

Entomological data are often overdispersed, characterised by a larger variance than assumed by simple standard models. It is important to model overdispersion properly in order to avoid incorrect and misleading inferences. Outcomes of interest are often in the form of counts or proportions and we present extended models that incorporate overdispersion, methods to assess its impact and model goodness-of-fit, and techniques to test treatment differences in the presence of overdispersion.Not peer reviewe