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The problem of computing the distribution of quadratic forms in normal variables has a long tradition in the statistical literature. Well-established numerical algorithms that deal with this task rely on the inversion of Fourier transforms or series representations. In this article, the Mellin transform is proposed as a tool to compute both the density and the cumulative distribution functions of a positive definite quadratic form: an outline of the numerical algorithm is presented, providing details on the error analysis. The algorithm's characteristics allow us to propose an efficient way to compute the random variables' quantiles. From the theoretical point of view, the analytic properties of the Mellin transform are exploited to provide a novel representation of the distribution of the ratio of independent quadratic forms as a mixture of beta random variables of the second kind. Moreover, algorithms are proposed for computations related to ratios of both independent and dependent quadratic forms. The methods are tested and compared to popular numerical algorithms in terms of computational times and accuracy. The R package QF implementing all the proposed algorithms is also made available. for this article are available online. [ABSTRACT FROM AUTHOR]

Estimating poverty and inequality parameters for small sub‐populations with adequate precision is often beyond the reach of ordinary survey‐weighted methods because of small sample sizes. In small area estimation, survey data and auxiliary information are combined, in most cases using a model. In this paper, motivated by the analysis of EU‐SILC data for Italy, we target the estimation of a selection of poverty and inequality indicators, that is mean, headcount ratio and quintile share ratio, adopting a Bayesian approach. We consider unit‐level models specified on the log transformation of a skewed variable (equivalized income). We show how a finite mixture of log‐normals provides a substantial improvement in the quality of fit with respect to a single log‐normal model. Unfortunately, working with these distributions leads, for some estimands, to the non‐existence of posterior moments whenever priors for the variance components are not carefully chosen, as our theoretical results show. To allow the use of moments in posterior summaries, we recommend generalized inverse Gaussian distributions as priors for variance components, guiding the choice of hyperparameters. [ABSTRACT FROM AUTHOR]

The log‐normal distribution is very popular for modeling positive right‐skewed data and represents a common distributional assumption in many environmental applications. Here we consider the estimation of quantiles of this distribution from a Bayesian perspective. We show that the prior on the variance of the log of the variable is relevant for the properties of the posterior distribution of quantiles. Popular choices for this prior, such as the inverse gamma, lead to posteriors without finite moments. We propose the generalized inverse Gaussian and show that a restriction on the choice of one of its parameters guarantees the existence of posterior moments up to a prespecified order. In small samples, a careful choice of the prior parameters leads to point and interval estimators of the quantiles with good frequentist properties, outperforming those currently suggested by the frequentist literature. Finally, two real examples from environmental monitoring and occupational health frameworks highlight the improvements of our methodology, especially in a small sample situation. [ABSTRACT FROM AUTHOR]

Research describes the physiological properties, surface protein profiles, and species-specific DNA probe hybridization of 119 Lactobacillus helveticus strains from Provolone, Grana Padano, and Parmigiano Reggiano whey types using the classification tree method. This method enables identification of the main characteristics that discriminate biotypes and phenotypes.

Abstract: Hierarchical models are popular in many applied statistics fields including Small Area Estimation. One well known model employed in this particular field is the Fay–Herriot model, in which unobservable parameters are assumed to be Gaussian. In Hierarchical models assumptions about unobservable quantities are difficult to check. For a special case of the Fay–Herriot model, Sinharay and Stern [2003. Posterior predictive model checking in Hierarchical models. J. Statist. Plann. Inference 111, 209–221] showed that violations of the assumptions about the random effects are difficult to detect using posterior predictive checks. In this present paper we consider two extensions of the Fay–Herriot model in which the random effects are assumed to be distributed according to either an exponential power (EP) distribution or a skewed EP distribution. We aim to explore the robustness of the Fay–Herriot model for the estimation of individual area means as well as the empirical distribution function of their ‘ensemble’. Our findings, which are based on a simulation experiment, are largely consistent with those of Sinharay and Stern as far as the efficient estimation of individual small area parameters is concerned. However, when estimating the empirical distribution function of the ‘ensemble’ of small area parameters, results are more sensitive to the failure of distributional assumptions. [Copyright &y& Elsevier]

Disease mapping studies have been widely performed at univariate level, that is considering only one disease in the estimated models. Nonetheless, simultaneous modelling of different diseases can be a valuable tool both from the epidemiological and from the statistical point of view. In this paper we propose a model for multivariate disease mapping that generalizes the univariate conditional auto-regressive distribution. The proposed model is proven to be an effective alternative to existing multivariate models, mainly because it overcome some restrictive hypotheses underlying models previously proposed in this context. Model performances are checked via a simulation study and via application to a case study. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The purpose of this study was to investigate the effect of dietary vitamin E or EconomasE™ supplementation on the growth of several background/pathogenic bacteria on rabbit carcasses and hamburgers during refrigerated storage. For 51 days, 270 New Zealand rabbits received either a basal diet, or experimental diets enriched with 100 or 200 mg/kg of vitamin E or EconomasE™. The bacteria studied were Salmonella , Listeria monocytogenes , Pseudomonas , Enterobacteriaceae , Escherichia coli , coagulase-positive staphylococci, plus both mesophilic and psychrotrophic aerobes. The growth of Listeria monocytogenes on contaminated patties was evaluated through a challenge test. The potential protective or antimicrobial effect of vitamin E or EconomasE™ on Listeria monocytogenes or Pseudomonas aeruginosa was assessed in vitro . Diet did not influence the concentrations of bacteria found on rabbit carcasses and developing on hamburgers. Vitamin E ( in vivo and in vitro ) and EconomasE™ in vivo had a protective antioxidant role, while EconomasE™ in vitro had strong antibacterial activity against Listeria monocytogenes, but not against Pseudomonas aeruginosa . [ABSTRACT FROM AUTHOR]