The beta Laplace distribution

The Laplace distribution is one of the earliest distributions in probability theory. For the first time, based on this distribution, we propose the so-called beta Laplace distribution, which extends the Laplace distribution. Various structural properties of the new distribution are derived, including expansions for its moments, moment generating function, moments of the order statistics, and so forth. We discuss maximum likelihood estimation of the model parameters and derive the observed information matrix. The usefulness of the new model is illustrated by means of a real data set. (C) 2011 Elsevier B.V. All rights reserved.

Numerical study of tensile tests conducted on systems with elastic-plastic films deposited onto elastic-plastic substrates

In this work, a series of two-dimensional plane-strain finite element analyses was conducted to further understand the stress distribution during tensile tests on coated systems. Besides the film and the substrate, the finite element model also considered a number of cracks perpendicular to the film/substrate interface. Different from analyses commonly found in the literature, the mechanical behavior of both film and substrate was considered elastic-perfectly plastic in part of the analyses. Together with the film yield stress and the number of film cracks, other variables that were considered were crack tip geometry, the distance between two consecutive cracks and the presence of an interlayer. The analysis was based on the normal stresses parallel to the loading axis (sigma(xx)), which are responsible for cohesive failures that are observed in the film during this type of test. Results indicated that some configurations studied in this work have significantly reduced the value of sigma(xx) at the film/substrate interface and close to the pre-defined crack tips. Furthermore, in all the cases studied the values of sigma(xx) were systematically larger at the film/substrate interface than at the film surface. (C) 2010 Elsevier B.V. All rights reserved.

Validated spectrophotometric and spectrofluorimetric methods for determination of chloroaluminum phthalocyanine in nanocarriers

UV-VIS-Spectrophotometric and spectrofluorimetric methods have been developed and validated allowing the quantification of chloroaluminum phthalocyanine (CIAIPc) in nanocarriers. In order to validate the methods, the linearity, limit of detection (LOD), limit of quantification (LOQ), precision, accuracy, and selectivity were examined according to USP 30 and ICH guidelines. Linearities range were found between 0.50-3.00 mu g.mL(-1) (Y=0.3829 X [CIAIPc, mu g.mL(-1)] + 0.0126; r=0.9992) for spectrophotometry, and 0.05-1.00 mu g.mL(-1) (Y=2.24 x 10(6) X [CIAIPc, mu g.L(-1)] + 9.74 x 10(4); r=0.9978) for spectrofluorimetry. In addition, ANOVA and Lack-of-fit tests demonstrated that the regression equations were statistically significant (p<0.05), and the resulting linear model is fully adequate for both analytical methods. The LOD values were 0.09 and 0.01 mu g.mL(-1), while the LOCI were 0.27 and 0.04 mu g.mL(-1) for spectrophotometric and spectrofluorimetric methods, respectively. Repeatability and intermediate precision for proposed methods showed relative standard deviation (RSD) between 0.58% to 4.80%. The percent recovery ranged from 98.9% to 102.7% for spectrophotometric analyses and from 94.2% to 101.2% for spectrofluorimetry. No interferences from common excipients were detected and both methods were considered specific. Therefore, the methods are accurate, precise, specific, and reproducible and hence can be applied for quantification of CIAIPc in nanoemulsions (NE) and nanocapsules (NC).

Comparison of different nonlinear functions to describe Nelore cattle growth

This work aims to compare different nonlinear functions for describing the growth curves of Nelore females. The growth curve parameters, their (co) variance components, and environmental and genetic effects were estimated jointly through a Bayesian hierarchical model. In the first stage of the hierarchy, 4 nonlinear functions were compared: Brody, Von Bertalanffy, Gompertz, and logistic. The analyses were carried out using 3 different data sets to check goodness of fit while having animals with few records. Three different assumptions about SD of fitting errors were considered: constancy throughout the trajectory, linear increasing until 3 yr of age and constancy thereafter, and variation following the nonlinear function applied in the first stage of the hierarchy. Comparisons of the overall goodness of fit were based on Akaike information criterion, the Bayesian information criterion, and the deviance information criterion. Goodness of fit at different points of the growth curve was compared applying the Gelfand`s check function. The posterior means of adult BW ranged from 531.78 to 586.89 kg. Greater estimates of adult BW were observed when the fitting error variance was considered constant along the trajectory. The models were not suitable to describe the SD of fitting errors at the beginning of the growth curve. All functions provided less accurate predictions at the beginning of growth, and predictions were more accurate after 48 mo of age. The prediction of adult BW using nonlinear functions can be accurate when growth curve parameters and their (co) variance components are estimated jointly. The hierarchical model used in the present study can be applied to the prediction of mature BW in herds in which a portion of the animals are culled before adult age. Gompertz, Von Bertalanffy, and Brody functions were adequate to establish mean growth patterns and to predict the adult BW of Nelore females. The Brody model was more accurate in predicting the birth weight of these animals and presented the best overall goodness of fit.

Measuring Bond Strength Between Fiber Post and Root Dentin: A Comparison of Different Tests

Purpose The aim of this study was to evaluate the ability of bond strength tests to accurately measure the bond strength of fiber posts luted into root canals Materials and Methods The test methods studied were hourglass microtensile (HM), push-out (PS), modified push out (MP) and pull out (PL) The evaluated parameters were bond strength values, reliability (using Weibull analysis), failure mode (using confocal microscopy), and stress distribution (using finite element analysis) Forty human intact single rooted and endodontically treated teeth were divided into four groups Each group was assigned one of the test methods The samples in the HM and PS groups were 1 0 +/- 0 1 mm thick, the HM samples were hourglass shaped and the PS samples were disk shaped For the PL and MP groups, each 1 mm dentin slice was luted with a fiber post piece Three dimensional models of each group were made and stress was analyzed based on Von Mises criteria Results PL provided the highest values of bond strength followed by MP both of which also had greater amounts of adhesive failures PS showed the highest frequency of cohesive failures MP showed a more homogeneous stress distribution and a higher Weibull modulus Conclusion The specimen design directly influences the biomechanical behavior of bond strength tests

Research on Candida dubliniensis in a Brazilian yeast collection obtained from cardiac transplant, tuberculosis, and HIV-positive patients, and evaluation of phenotypic tests using agar screening methods

The aim of this study was to research Candida dubliniensis among isolates present in a Brazilian yeast collection and to evaluate the main phenotypic methods for discrimination between C. albicans and C. dubliniensis from oral cavity. A total of 200 isolates, presumptively identified as C. albicans or C. dubliniensis obtained from heart transplant patients under immunosuppressive therapy, tuberculosis patients under antibiotic therapy, HIV-positive patients under antiretroviral therapy, and healthy subjects, were analyzed using the following phenotypic tests: formation and structural arrangement of chlamydospores on corn meal agar, casein agar, tobacco agar, and sunflower seed agar; growth at 45 degrees C; and germ tube formation. All strains were analyzed by polymerase chain reaction (PCR). In a preliminary screen for C. dubliniensis, 48 of the 200 isolates on corn meal agar, 30 of the 200 on casein agar, 16 of the 200 on tobacco agar, and 15 of the 200 on sunflower seed agar produced chlamydoconidia; 27 of the 200 isolates showed no or poor growth at 45 degrees C. All isolates were positive for germ tube formation. These isolates were considered suggestive of C. dubliniensis. All of them were subjected to PCR analysis using C. dubliniensis-specific primers. C. dubliniensis isolates were not found. C. dubliniensis isolates were not recovered in this study done with immunocompromised patients. Sunflower seed agar was the medium with the smallest number of isolates of C. albicans suggestive of C. dubliniensis. None of the phenotypic methods was 100% effective for discrimination between C. albicans and C. dubliniensis. (C) 2011 Elsevier Inc. All rights reserved.

Size and power properties of some tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the non-null distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the Birnbaum-Saunders regression model. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the shape parameter. Monte Carlo simulation is presented in order to compare the finite-sample performance of these tests. We also present two empirical applications. (C) 2010 Elsevier B.V. All rights reserved.

Local power of some tests in exponential family nonlinear models

In this paper we obtain asymptotic expansions up to order n(-1/2) for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in exponential family nonlinear models (Cordeiro and Paula, 1989), under a sequence of Pitman alternatives. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the dispersion parameter, thus generalising the results given in Cordeiro et al. (1994) and Ferrari et al. (1997). We also present Monte Carlo simulations in order to compare the finite-sample performance of these tests. (C) 2010 Elsevier B.V. All rights reserved.

Solvatochromism in Binary Mixtures: First Report on a Solvation Free Energy Relationship between Solvent Exchange Equilibrium Constants and the Properties of the Medium

We have employed UV-vis spectroscopy in order to investigate details of the solvation of six solvatochromic indicators, hereafter designated as ""probes"", namely, 2,6-diphenyl-4-(2,4,6-triphenylpyridinium-1-yl) phenolate (RB); 4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePM; 1-methylquinolinium-8-olate, QB; 2-bromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr, 2,6-dichloro-4-(2,4,6-triphenylpyridinium-1-yl) phenolate (WB); and 2,6-dibromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr,, respectively. These can be divided into three pairs, each includes two probes of similar pK(a) in water and different lipophilicity. Solvation has been studied in binary mixtures, BMs, of water, W, with 12 protic organic solvents, S, including mono- and bifunctional alcohols (2-alkoxyethanoles, unsaturated and chlorinated alcohols). Each medium was treated as a mixture of S, W, and a complex solvent, S-W, formed by hydrogen bonding. Values of lambda(max) (of the probe intramolecular charge transfer) were converted into empirical polarity scales, E(T)(probe) in kcal/mol, whose values were correlated with the effective mole fraction of water in the medium, chi w(effective). This correlation furnished three equilibrium constants for the exchange of solvents in the probe solvation shell; phi(W/S) (W substitutes S): phi(S-W/W) (S-W substitutes W), and phi(S-W/S) (S-W substitutes S), respectively. The values of these constants depend on the physicochemical properties of the probe and the medium. We tested, for the first time, the applicability of a new solvation free energy relationship: phi = constant + a alpha(BM) + b beta(BM) + s(pi*(BM) + d delta) + p log P(BM), where a, b, s, and p are regression coefficients alpha(BM), beta(BM), and pi*(BM) are solvatochromic parameters of the BM, delta is a correction term for pi*, and log P is an empirical scale of lipophilicity. Correlations were carried out with two-, three-, and four-medium descriptors. In all cases, three descriptors gave satisfactory correlations; use of four parameters gave only a marginal increase of the goodness of fit. For phi(W/S), the most important descriptor was found to be the lipophilicity of the medium; for phi(S-W/W) and phi(S-W/S), solvent basicity is either statistically relevant or is the most important descriptor. These responses are different from those of E(T)(probe) of many solvatochromic indicators in pure solvents, where the importance of solvent basicity is usually marginal, and can be neglected.

Solvation in Pure Liquids: What Can Be Learned from the Use of Pairs of Indicators?

The solvation of six solvatochromic probes in a large number of solvents (33-68) was examined at 25 degrees C. The probes employed were the following: 2,6-diphenyl-4-(2,4,6-triphenylpyridinium-1-yl) phenolate (RB); 4-[(E)2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePM; 1-methylquinolinium-8-olate, QB; 2-bromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr, 2,6-dichloro-4-(2,4,6-triphenyl pyridinium-1-yl) phenolate (WB); and 2,6-dibromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr(2), respectively. Of these, MePMBr is a novel compound. They can be grouped in three pairs, each with similar pK(a) in water but with different molecular properties, for example, lipophilicity and dipole moment. These pairs are formed by RB and MePM; QB and MePMBr; WB and MePMBr(2), respectively. Theoretical calculations were carried out in order to calculate their physicochemical properties including bond lengths, dihedral angles, dipole moments, and wavelength of absorption of the intramolecular charge-transfer band in four solvents, water, methanol, acetone, and DMSO, respectively. The data calculated were in excellent agreement with available experimental data, for example, bond length and dihedral angles. This gives credence to the use of the calculated properties in explaining the solvatochromic behaviors observed. The dependence of an empirical solvent polarity scale E(T)(probe) in kcal/mol on the physicochemical properties of the solvent (acidity, basicity, and dipolarity/polarizability) and those of the probes (pK(a), and dipole moment) was analyzed by using known multiparameter solvation equations. For each pair of probes, values of E(T)(probe) (for example, E(T)(MePM) versus E(T)(RB)) were found to be linearly correlated with correlation coefficients, r, between 0.9548 and 0.9860. For the mercyanine series, the values of E(T)(probe) also correlated linearly, with (r) of 0.9772 (MePMBr versus MePM) and 0.9919 (MePMBr(2) versus MePM). The response of each pair of probes (of similar pK(a)) to solvent acidity is the same, provided that solute-solvent hydrogen-bonding is not seriously affected by steric crowding (as in case of RB). We show, for the first time, that the response to solvent dipolarity/polarizability is linearly correlated to the dipole moment of the probes. The successive introduction of bromine atoms in MePM (to give MePMBr, then MePMBr(2)) leads to the following linear decrease: pK(a) in water, length of the phenolate oxygen-carbon bond, length of the central ethylenic bond, susceptibility to solvent acidity, and susceptibility to solvent dipolarity/polarizability. Thus studying the solvation of probes whose molecular structures are varied systematically produces a wealth of information on the effect of solute structure on its solvation. The results of solvation of the present probes were employed in order to test the goodness of fit of two independent sets of solvent solvatochromic parameters.

TESTING STATISTICAL HYPOTHESIS ON RANDOM TREES AND APPLICATIONS TO THE PROTEIN CLASSIFICATION PROBLEM

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov-Smirnov-type goodness-of-fit test proposed by Balding et at. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford-Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton-Watson related processes.

Random number generators for the generalized Birnbaum-Saunders distribution

The generalized Birnbaum-Saunders distribution pertains to a class of lifetime models including both lighter and heavier tailed distributions. This model adapts well to lifetime data, even when outliers exist, and has other good theoretical properties and application perspectives. However, statistical inference tools may not exist in closed form for this model. Hence, simulation and numerical studies are needed, which require a random number generator. Three different ways to generate observations from this model are considered here. These generators are compared by utilizing a goodness-of-fit procedure as well as their effectiveness in predicting the true parameter values by using Monte Carlo simulations. This goodness-of-fit procedure may also be used as an estimation method. The quality of this estimation method is studied here. Finally, through a real data set, the generalized and classical Birnbaum-Saunders models are compared by using this estimation method.

An R implementation for generalized Birnbaum-Saunders distributions

The Birnbaum-Saunders (BS) model is a positively skewed statistical distribution that has received great attention in recent decades. A generalized version of this model was derived based on symmetrical distributions in the real line named the generalized BS (GBS) distribution. The R package named gbs was developed to analyze data from GBS models. This package contains probabilistic and reliability indicators and random number generators from GBS distributions. Parameter estimates for censored and uncensored data can also be obtained by means of likelihood methods from the gbs package. Goodness-of-fit and diagnostic methods were also implemented in this package in order to check the suitability of the GBS models. in this article, the capabilities and features of the gbs package are illustrated by using simulated and real data sets. Shape and reliability analyses for GBS models are presented. A simulation study for evaluating the quality and sensitivity of the estimation method developed in the package is provided and discussed. (C) 2008 Elsevier B.V. All rights reserved.

Hypothesis testing in an errors-in-variables model with heteroscedastic measurement errors

In many epidemiological studies it is common to resort to regression models relating incidence of a disease and its risk factors. The main goal of this paper is to consider inference on such models with error-prone observations and variances of the measurement errors changing across observations. We suppose that the observations follow a bivariate normal distribution and the measurement errors are normally distributed. Aggregate data allow the estimation of the error variances. Maximum likelihood estimates are computed numerically via the EM algorithm. Consistent estimation of the asymptotic variance of the maximum likelihood estimators is also discussed. Test statistics are proposed for testing hypotheses of interest. Further, we implement a simple graphical device that enables an assessment of the model`s goodness of fit. Results of simulations concerning the properties of the test statistics are reported. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease. Copyright (C) 2008 John Wiley & Sons, Ltd.

Generalized Birnbaum-Saunders distributions applied to air pollutant concentration

The generalized Birnbaum-Saunders (GBS) distribution is a new class of positively skewed models with lighter and heavier tails than the traditional Birnbaum-Saunders (BS) distribution, which is largely applied to study lifetimes. However, the theoretical argument and the interesting properties of the GBS model have made its application possible beyond the lifetime analysis. The aim of this paper is to present the GBS distribution as a useful model for describing pollution data and deriving its positive and negative moments. Based on these moments, we develop estimation and goodness-of-fit methods. Also, some properties of the proposed estimators useful for developing asymptotic inference are presented. Finally, an application with real data from Environmental Sciences is given to illustrate the methodology developed. This example shows that the empirical fit of the GBS distribution to the data is very good. Thus, the GBS model is appropriate for describing air pollutant concentration data, which produces better results than the lognormal model when the administrative target is determined for abating air pollution. Copyright (c) 2007 John Wiley & Sons, Ltd.