Model Comparison of Coordinate-Free Multivariate Skewed Distributions with an Application to Stochastic Frontiers

We consider classes of multivariate distributions which can model skewness and are closed under orthogonal transformations. We review two classes of such distributions proposed in the literature and focus our attention on a particular, yet quite flexible, subclass of one of these classes. Members of this subclass are defined by affine transformations of univariate (skewed) distributions that ensure the existence of a set of coordinate axes along which there is independence and the marginals are known analytically. The choice of an appropriate m-dimensional skewed distribution is then restricted to the simpler problem of choosing m univariate skewed distributions. We introduce a Bayesian model comparison setup for selection of these univariate skewed distributions. The analysis does not rely on the existence of moments (allowing for any tail behaviour) and uses equivalent priors on the common characteristics of the different models. Finally, we apply this framework to multi-output stochastic frontiers using data from Dutch dairy farms.Coordinate-free distributions, dairy farm, multivariate skewness, orthogonal transformation, stochastic frontier.

A Constructive Representation of Univariate Skewed Distributions

We introduce a general perspective on the introduction of skewness into symmetric distributions. Making use of inverse probability integral transformations we provide a constructive representation of skewed distributions, where the skewing mechanism and the original symmetric distributions are specified separately. We study the effects of the skewing mechanism on \emph{e.g.} modality, tail behaviour and the amount of skewness generated. In light of the constructive representation, we review a number of characteristics of three classes of skew distributions previously defined in the literature. The representation is also used to introduce two novel classes of skewed distributions. Finally, we incorporate the different classes of distributions into a Bayesian linear regression framework and analyse their differences and similarities.Arnold and Groeneveld skewness measure, Bayesian regression model, inverse probability integral transformation, modality, skewing mechanism, tail behaviour

Bayesian Multivariate Regression Analysis with a New Class of Skewed Distributions

In this paper, we introduce a novel class of skewed multivariate distributions and, more generally, a method of building such a class on the basis of univariate skewed distributions. The method is based on a general linear transformation of a multidimensional random variable with independent components, each with a skewed distribution. Our proposed class of multivariate skewed distributions has a simple, intuitive form for the pdf, moment existence only depends on the existence of the moments of the underlying symmetric univariate distributions, and we avoid any conditioning on unobserved variables. In addition, we can freely allow for any mean and covariance structure in combination with any magnitude and direction of skewness. In order to deal with both skewness and fat tails, we introduce multivariate skewed regression models with fat tails, based on Student distributions. We present two main classes of such distributions, one of which is novel even under symmetry. Under standard non-informative priors on both regression and scale parameters, we derive conditions for propriety of the posterior and for existence of posterior moments. We describe MCMC samplers for conducting Bayesian inference and analyse two applications, one concerning the distribution of various measures of firm size and another on a set of biomedical data.Asymmetric distributions; Heavy tails; Linear regression model; Mardia's measure of skewness; Orthogonal matrices; Posterior propriety.

Mössbauer and magnetic study of Co x Fe3−x O4 nanoparticles

Magnetic nanoparticles of cobalt ferrites Co x Fe3−x O4 (x = 1 or 2) have been obtained either by mechanical milling or thermal treatment of pre-prepared layered double hydroxide carbonate x-LDH–CO3. Mechanical milling of the 1-LDH–CO3 leads to the large-scale preparation of nearly spherical nanoparticles of CoFe2O4, the size of which (5 to 20 nm) is controlled by the treatment time. Core-shell structure with surface spin-canting has been considered for the nanoparticles formed to explain the observed hysteresis loop shift (from ZFC–FC) in the magnetic properties. Annealing treatment of the 2-LDH–CO3 below 673 K results in the formation of nearly spherical pure Co2FeO4 nanoparticles. At 673 K and above, the LDH decomposition leads to the formation of a mixture of both spinels phases Co2FeO4 and CoFe2O4, the amount of the latter increases with annealing temperature. Unusually high magnetic hardness characterized by a 22 kOe coercive field at 1.8 K has been observed, which reflects the high intrinsic anisotropy for Co2FeO4

Interferência de plantas daninhas na cultura de algodão em sistema de plantio direto

Em experimento conduzido em solo de textura argilosa, localizado no município de Viçosa-MG, durante o ano agrícola 1998/1999, avaliaram-se os períodos de convivência de plantas daninhas com a cultura do algodão conduzida em sistema de plantio direto. Foram avaliados os tratamentos: períodos de 0, 15, 30, 45, 60 e 75 dias após a semeadura da cultura do algodão em convivência com as plantas daninhas; depois desse período a cultura foi mantida livre da competição com as plantas daninhas até a colheita, em delineamento de blocos ao acaso, com quatro repetições. As parcelas foram constituídas de seis fileiras com 4 m de comprimento, espaçadas de 0,9 m, com seis plantas por metro. As plantas daninhas foram avaliadas ao final de cada período de convivência, determinando-se o número e a biomassa seca da parte aérea de cada espécie. Também foram avaliadas na cultura a altura média das plantas, aos 125 dias após a emergência (DAE), o número de maçãs por planta, o número de nós até a inserção do primeiro ramo frutífero e, na colheita, a produtividade de algodão em caroço. O acúmulo médio de biomassa seca do total de plantas daninhas foi de 4,7 g m-2 dia-1. Comparando os tratamentos com e sem interferência, verificou-se que a presença das plantas daninhas durante todo o ciclo da cultura aumentou o número de nós até a inserção do primeiro ramo frutífero e reduziu o número de maçãs e a altura das plantas, além de reduzir a produtividade de algodão em caroço em 81,2%. O período que antecede a interferência das plantas daninhas (PAI), considerando uma perda tolerável de 5% na produtividade de algodão em caroço, foi de 14 DAE.An experiment was conducted in clay soil texture, in Viçosa-MG, Brazil, during the growing season 1989/1999, to evaluate the periods of weed coexistence in a cotton crop under no-tillage. The treatments were: 0, 15, 30, 45, 60 and 75 days after crop seeding under weed coexistence, and maintained weed free until crop harvest. The plots consisted of six rows 4 m long, and 0.9 m spaced, with six plants per meter. At the end of each coexistence period, the weeds were evaluated, by determining the number of species and shoot dry matter weight. The average crop plant height was also evaluated; 125 days after emergence (DAE), boll numbers per plant, and node numbers until insertion of the first fruitful branch were also evaluated, while cotton productivity was evaluated at harvesting. The average accumulation of the total dry matter of weeds was 4.7 g m-2 day-1. When comparing the treatments with and without weed interference, it was observed that weed interference throughout the cycle increased the average node numbers until insertion of the first fruitful branch, but reduced the average boll numbers and height of the plants. Weed interference throughout the cotton plant cycle caused a reduction of 81.2% in cotton productivity. Considering the 5% loss in productivity as acceptable, the period previous to weed interference was14 DAE