An extension of the half-normal distribution

In this paper we introduce a new distribution, namely, the slashed half-normal distribution and it can be seen as an extension of the half-normal distribution. It is shown that the resulting distribution has more kurtosis than the ordinary half-normal distribution. Moments and some properties are derived for the new distribution. Moment estimators and maximum likelihood estimators can computed using numerical procedures. Results of two real data application are reported where model fitting is implemented by using maximum likelihood estimation. The applications illustrate the better performance of the new distribution.

Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353-365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R. B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362-1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis-Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271-275]. Our algorithm has only one Metropolis-Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146-178; R. J. Patz and B. W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342-366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599-607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models.

Probing the anomalous extinction of four young star clusters: the use of colour-excess, main-sequence fitting and fractal analysis

Aims. We studied four young star clusters to characterise their anomalous extinction or variable reddening and asses whether they could be due to contamination by either dense clouds or circumstellar effects. Methods. We evaluated the extinction law (R-V) by adopting two methods: (i) the use of theoretical expressions based on the colour-excess of stars with known spectral type; and (ii) the analysis of two-colour diagrams, where the slope of the observed colour distribution was compared to the normal distribution. An algorithm to reproduce the zero-age main-sequence (ZAMS) reddened colours was developed to derive the average visual extinction (A(V)) that provides the closest fit to the observational data. The structure of the clouds was evaluated by means of a statistical fractal analysis, designed to compare their geometric structure with the spatial distribution of the cluster members. Results. The cluster NGC 6530 is the only object of our sample affected by anomalous extinction. On average, the other clusters suffer normal extinction, but several of their members, mainly in NGC 2264, seem to have high R-V, probably because of circumstellar effects. The ZAMS fitting provides A(V) values that are in good agreement with those found in the literature. The fractal analysis shows that NGC 6530 has a centrally concentrated distribution of stars that differs from the substructures found in the density distribution of the cloud projected in the A(V) map, suggesting that the original cloud was changed by the cluster formation. However, the fractal dimension and statistical parameters of Berkeley 86, NGC 2244, and NGC 2264 indicate that there is a good cloud-cluster correlation, when compared to other works based on an artificial distribution of points.

Assessment of variance components in nonlinear mixed-effects elliptical models

The issue of assessing variance components is essential in deciding on the inclusion of random effects in the context of mixed models. In this work we discuss this problem by supposing nonlinear elliptical models for correlated data by using the score-type test proposed in Silvapulle and Silvapulle (1995). Being asymptotically equivalent to the likelihood ratio test and only requiring the estimation under the null hypothesis, this test provides a fairly easy computable alternative for assessing one-sided hypotheses in the context of the marginal model. Taking into account the possible non-normal distribution, we assume that the joint distribution of the response variable and the random effects lies in the elliptical class, which includes light-tailed and heavy-tailed distributions such as Student-t, power exponential, logistic, generalized Student-t, generalized logistic, contaminated normal, and the normal itself, among others. We compare the sensitivity of the score-type test under normal, Student-t and power exponential models for the kinetics data set discussed in Vonesh and Carter (1992) and fitted using the model presented in Russo et al. (2009). Also, a simulation study is performed to analyze the consequences of the kurtosis misspecification.

A log-Birnbaum-Saunders regression model with asymmetric errors

This paper introduces a skewed log-Birnbaum-Saunders regression model based on the skewed sinh-normal distribution proposed by Leiva et al. [A skewed sinh-normal distribution and its properties and application to air pollution, Comm. Statist. Theory Methods 39 (2010), pp. 426-443]. Some influence methods, such as the local influence and generalized leverage, are presented. Additionally, we derived the normal curvatures of local influence under some perturbation schemes. An empirical application to a real data set is presented in order to illustrate the usefulness of the proposed model.

Using complex networks to quantify consistency in the use of words

In this paper we have quantified the consistency of word usage in written texts represented by complex networks, where words were taken as nodes, by measuring the degree of preservation of the node neighborhood. Words were considered highly consistent if the authors used them with the same neighborhood. When ranked according to the consistency of use, the words obeyed a log-normal distribution, in contrast to Zipf's law that applies to the frequency of use. Consistency correlated positively with the familiarity and frequency of use, and negatively with ambiguity and age of acquisition. An inspection of some highly consistent words confirmed that they are used in very limited semantic contexts. A comparison of consistency indices for eight authors indicated that these indices may be employed for author recognition. Indeed, as expected, authors of novels could be distinguished from those who wrote scientific texts. Our analysis demonstrated the suitability of the consistency indices, which can now be applied in other tasks, such as emotion recognition.

On Wald Residuals in Generalized Linear Models

A rigorous asymptotic theory for Wald residuals in generalized linear models is not yet available. The authors provide matrix formulae of order O(n(-1)), where n is the sample size, for the first two moments of these residuals. The formulae can be applied to many regression models widely used in practice. The authors suggest adjusted Wald residuals to these models with approximately zero mean and unit variance. The expressions were used to analyze a real dataset. Some simulation results indicate that the adjusted Wald residuals are better approximated by the standard normal distribution than the Wald residuals.

STOCHASTIC MODEL FOR SIMULATING MAIZE YIELD

Maize is one of the most important crops in the world. The products generated from this crop are largely used in the starch industry, the animal and human nutrition sector, and biomass energy production and refineries. For these reasons, there is much interest in figuring the potential grain yield of maize genotypes in relation to the environment in which they will be grown, as the productivity directly affects agribusiness or farm profitability. Questions like these can be investigated with ecophysiological crop models, which can be organized according to different philosophies and structures. The main objective of this work is to conceptualize a stochastic model for predicting maize grain yield and productivity under different conditions of water supply while considering the uncertainties of daily climate data. Therefore, one focus is to explain the model construction in detail, and the other is to present some results in light of the philosophy adopted. A deterministic model was built as the basis for the stochastic model. The former performed well in terms of the curve shape of the above-ground dry matter over time as well as the grain yield under full and moderate water deficit conditions. Through the use of a triangular distribution for the harvest index and a bivariate normal distribution of the averaged daily solar radiation and air temperature, the stochastic model satisfactorily simulated grain productivity, i.e., it was found that 10,604 kg ha(-1) is the most likely grain productivity, very similar to the productivity simulated by the deterministic model and for the real conditions based on a field experiment.

Likelihood-based inference for power distributions

This paper considers likelihood-based inference for the family of power distributions. Widely applicable results are presented which can be used to conduct inference for all three parameters of the general location-scale extension of the family. More specific results are given for the special case of the power normal model. The analysis of a large data set, formed from density measurements for a certain type of pollen, illustrates the application of the family and the results for likelihood-based inference. Throughout, comparisons are made with analogous results for the direct parametrisation of the skew-normal distribution.

Minimal alterations on the enamel surface by micro-abrasion: in vitro roughness and wear assessments

Objective: To evaluate the in vitro changes on the enamel surface after a micro-abrasion treatment promoted by different products. Material and Methods: Fifty (50) fragments of bovine enamel (15 mm × 5 mm) were randomly assigned to five groups (n=10) according to the product utilized: G1 (control)= silicone polisher (TDV), G2= 37% phosphoric acid (3M/ESPE) + pumice stone (SS White), G3= Micropol (DMC Equipment), G4= Opalustre (Ultradent) and G5= Whiteness RM (FGM Dental Products). Roughness and wear were the responsible variables used to analyze these surfaces in four stages: baseline, 60 s and 120 s after the micro-abrasion and after polishing, using a Hommel Tester T1000 device. After the tests, a normal distribution of data was verified, with repeated ANOVA analyses (p?0.05) which were used to compare each product in different stages. One-way ANOVA and Tukey tests were applied for individual comparisons between the products in each stage (p?0.05). Results: Means and standard deviations of roughness and wear (µm) after all the promoted stages were: G1=7.26(1.81)/13.16(2.67), G2=2.02(0.62)/37.44(3.33), G3=1.81(0.91)/34.93(6.92), G4=1.92(0.29)/38.42(0.65) and G5=1.98(0.53)/33.45(2.66). At 60 seconds, all products tended to produce less surface roughness with a variable gradual decrease over time. After polishing, there were no statistically significant differences between the groups, except for G1. Independent of the product utilized, the enamel wear occurred after the micro-abrasion. Conclusions: In this in vitro study, enamel micro-abrasion presented itself as a conservative approach, regardless of the type of the paste compound utilized. These products promoted minor roughness alterations and minimal wear. The use of phosphoric acid and pumice stone showed similar results to commercial products for the micro-abrasion with regard to the surface roughness and wear.

Spatial variability of leaf nutrient contents in a drip irrigated citrus orchard

This study aimed to evaluate the spatial variability of leaf content of macro and micronutrients. The citrus plants orchard with 5 years of age, planted at regular intervals of 8 x 7 m, was managed under drip irrigation. Leaf samples were collected from each plant to be analyzed in the laboratory. Data were analyzed using the software R, version 2.5.1 Copyright (C) 2007, along with geostatistics package GeoR. All contents of macro and micronutrients studied were adjusted to normal distribution and showed spatial dependence.The best-fit models, based on the likelihood, for the macro and micronutrients were the spherical and matern. It is suggest for the macronutrients nitrogen, phosphorus, potassium, calcium, magnesium and sulfur the minimum distances between samples of 37; 58; 29; 63; 46 and 15 m respectively, while for the micronutrients boron, copper, iron, manganese and zinc, the distances suggests are 29; 9; 113; 35 and 14 m, respectively.

Multivariate gene expression analysis reveals functional connectivity changes between normal/tumoral prostates

Abstract Background Prostate cancer is a leading cause of death in the male population, therefore, a comprehensive study about the genes and the molecular networks involved in the tumoral prostate process becomes necessary. In order to understand the biological process behind potential biomarkers, we have analyzed a set of 57 cDNA microarrays containing ~25,000 genes. Results Principal Component Analysis (PCA) combined with the Maximum-entropy Linear Discriminant Analysis (MLDA) were applied in order to identify genes with the most discriminative information between normal and tumoral prostatic tissues. Data analysis was carried out using three different approaches, namely: (i) differences in gene expression levels between normal and tumoral conditions from an univariate point of view; (ii) in a multivariate fashion using MLDA; and (iii) with a dependence network approach. Our results show that malignant transformation in the prostatic tissue is more related to functional connectivity changes in their dependence networks than to differential gene expression. The MYLK, KLK2, KLK3, HAN11, LTF, CSRP1 and TGM4 genes presented significant changes in their functional connectivity between normal and tumoral conditions and were also classified as the top seven most informative genes for the prostate cancer genesis process by our discriminant analysis. Moreover, among the identified genes we found classically known biomarkers and genes which are closely related to tumoral prostate, such as KLK3 and KLK2 and several other potential ones. Conclusion We have demonstrated that changes in functional connectivity may be implicit in the biological process which renders some genes more informative to discriminate between normal and tumoral conditions. Using the proposed method, namely, MLDA, in order to analyze the multivariate characteristic of genes, it was possible to capture the changes in dependence networks which are related to cell transformation.

Effects of myenteric denervation on extracellular matrix fibers and mast cell distribution in normal stomach and gastric lesions

Abstract Background In this study the effect of myenteric denervation induced by benzalconium chloride (BAC) on distribution of fibrillar components of extracellular matrix (ECM) and inflammatory cells was investigated in gastric carcinogenesis induced by N-methyl-N'-nitro-N-nitrosoguanidine (MNNG). Rats were divided in four experimental groups: non-denervated (I) and denervated stomach (II) without MNNG treatment; non-denervated (III) and denervated stomachs (IV) treated with MNNG. For histopathological, histochemical and stereological analysis, sections of gastric fragments were stained with Hematoxylin-Eosin, Picrosirius-Hematoxylin, Gomori reticulin, Weigert's Resorcin-Fuchsin, Toluidine Blue and Alcian-Blue/Safranin (AB-SAF). Results BAC denervation causes an increase in the frequency of reticular and elastic fibers in the denervated (group II) compared to the non-denervated stomachs (group I). The treatment of the animals with MNNG induced the development of adenocarcinomas in non-denervated and denervated stomachs (groups III and IV, respectively) with a notable increase in the relative volume of the stroma, the frequency of reticular fibers and the inflammatory infiltrate that was more intense in group IV. An increase in the frequency of elastic fibers was observed in adenocarcinomas of denervated (group IV) compared to the non-denervated stomachs (group III) that showed degradation of these fibers. The development of lesions (groups III and IV) was also associated with an increase in the mast cell population, especially AB and AB-SAF positives, the latter mainly in the denervated group IV. Conclusions The results show a strong association in the morphological alteration of the ECM fibrillar components, the increased density of mast cells and the development of tumors induced by MNNG in the non-denervated rat stomach or denervated by BAC. This suggests that the study of extracellular and intracellular components of tumor microenvironment contributes to understanding of tumor biology by action of myenteric denervation.

BENTHIC MACROFAUNA STRUCTURE IN THE NORTHEAST AREA OF TODOS OS SANTOS BAY, BAHIA STATE, BRAZIL: PATTERNS OF SPATIAL AND SEASONAL DISTRIBUTION

Structure of intertidal and subtidal benthic macrofauna in the northeastern region of Todos os Santos Bay (TSB), northeast Brazil, was investigated during a period of two years. Relationships with environmental parameters were studied through uni- and multivariate statistical analyses, and the main distributional patterns shown to be especially related to sediment type and content of organic fractions (Carbon, Nitrogen, Phosphorus), on both temporal and spatial scales. Polychaete annelids accounted for more than 70% of the total fauna and showed low densities, species richness and diversity, except for the area situated on the reef banks. These banks constitute a peculiar environment in relation to the rest of the region by having coarse sediments poor in organic matter and rich in biodetritic carbonates besides an abundant and diverse fauna. The intertidal region and the shallower area nearer to the oil refinery RLAM, with sediments composed mainly of fine sand, seem to constitute an unstable system with few highly dominant species, such as Armandia polyophthalma and Laeonereis acuta. In the other regions of TSB, where muddy bottoms predominated, densities and diversity were low, especially in the stations near the refinery. Here the lowest values of the biological indicators occurred together with the highest organic compound content. In addition, the nearest sites (stations 4 and 7) were sometimes azoic. The adjacent Caboto, considered as a control area at first, presented low density but intermediate values of species diversity, which indicates a less disturbed environment in relation to the pelitic infralittoral in front of the refinery. The results of the ordination analyses evidenced five homogeneous groups of stations (intertidal; reef banks; pelitic infralittoral; mixed sediments; Caboto) with different specific patterns, a fact which seems to be mainly related to granulometry and chemical sediment characteristics.

SPATIAL AND TEMPORAL DISTRIBUTION OF FISH IN PALMAS BAY, UBATUBA, BRAZIL

The aim of this study was to analyze the distribution and abundance of the fish fauna of Palmas bay on Anchieta Island in southeastern Brazil. Specimens were caught in the summer and winter of 1992, using an otter trawl at three locations in the bay. The specimens were caught in both the nighttime and daytime. Data on the water temperature and salinity were recorded for the characterization of the predominant water mass in the region, and sediment samples were taken for granulometric analysis. A total of 7 656 specimens (79 species), with a total weight of approximately 300 kg, were recorded. The most abundant species were Eucinostomus argenteus, Ctenosciaena gracilicirrhus, Haemulon steindachneri, Eucinostomus gula and Diapterus rhombeus, which together accounted for more than 73% of the sample. In general, the ecological indices showed no differences in the composition of species for the abiotic variables analyzed. The multivariate analysis showed that the variations in the distribution of the fish fauna were mainly associated with intra-annual differences in temperature and salinity, resulting from the presence of South Atlantic Central Water (SACW) in the area during the summer. The analysis also showed an association with the type of bottom and a lesser association with respect to the night/day periods.