The beta-Birnbaum-Saunders distribution An improved distribution for fatigue life modeling

Birnbaum and Saunders (1969a) introduced a probability distribution which is commonly used in reliability studies For the first time based on this distribution the so-called beta-Birnbaum-Saunders distribution is proposed for fatigue life modeling Various properties of the new model including expansions for the moments moment generating function mean deviations density function of the order statistics and their moments are derived We discuss maximum likelihood estimation of the model s parameters The superiority of the new model is illustrated by means of three failure real data sets (C) 2010 Elsevier B V All rights reserved

Assessment of production efficiency, physicochemical properties and storage stability of spray-dried chlorophyllide, a natural food colourant, using gum Arabic, maltodextrin and soy protein isolate-based carrier systems

P>The aim of this research was to study spray drying as potential action to protect chlorophyllide from environmental conditions for shelf-life extension and characterisation of the powders. Six formulations were prepared with 7.5 and 10 g of carrier agents [gum Arabic (GA), maltodextrin (MA) and soybean protein isolate (SPI)]/100 mL of chlorophyllide solutions. The powders were evaluated for morphological characteristics (SEM), particle size, water activity, moisture, density, hygroscopicity, cold water solubility, sorption isotherms, colour and stability, during 90 days. All the powders were highly soluble, with solubility values around 97%. A significant lower hygroscopicity was observed for GA powders, whilst the lower X(m) values obtained by GAB equation fitting of the sorption isotherms was observed for the 7.5 g MA/100 mL samples. All formulations, but the 1 (7.5 g SPI/100 mL of chlorophyllide), provided excellent stability to the chlorophyllide during 90 days of storage even at room temperature.

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.

Signed likelihood ratio tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders regression model is becoming increasingly popular in lifetime analyses and reliability studies. In this model, the signed likelihood ratio statistic provides the basis for testing inference and construction of confidence limits for a single parameter of interest. We focus on the small sample case, where the standard normal distribution gives a poor approximation to the true distribution of the statistic. We derive three adjusted signed likelihood ratio statistics that lead to very accurate inference even for very small samples. Two empirical applications are presented. (C) 2010 Elsevier B.V. All rights reserved.

Small-Sample Corrections for Score Tests in Birnbaum-Saunders Regressions

In this article, we deal with the issue of performing accurate small-sample inference in the Birnbaum-Saunders regression model, which can be useful for modeling lifetime or reliability data. We derive a Bartlett-type correction for the score test and numerically compare the corrected test with the usual score test and some other competitors.

Influence diagnostics in Birnbaum-Saunders nonlinear regression models

We consider the issue of assessing influence of observations in the class of Birnbaum-Saunders nonlinear regression models, which is useful in lifetime data analysis. Our results generalize those in Galea et al. [8] which are confined to Birnbaum-Saunders linear regression models. Some influence methods, such as the local influence, total local influence of an individual and generalized leverage are discussed. Additionally, the normal curvatures for studying local influence are derived under some perturbation schemes. We also give an application to a real fatigue data set.

Asymptotic skewness in Birnbaum-Saunders nonlinear regression models

The family of distributions proposed by Birnbaum and Saunders (1969) can be used to model lifetime data and it is widely applicable to model failure times of fatiguing materials. We give a simple matrix formula of order n(-1/2), where n is the sample size, for the skewness of the distributions of the maximum likelihood estimates of the parameters in Birnbaum-Saunders nonlinear regression models, recently introduced by Lemonte and Cordeiro (2009). The formula is quite suitable for computer implementation, since it involves only simple operations on matrices and vectors, in order to obtain closed-form skewness in a wide range of nonlinear regression models. Empirical and real applications are analyzed and discussed. (C) 2010 Elsevier B.V. All rights reserved.

An extension of the generalized Birnbaum-Saunders distribution

In this paper we present an extension of the generalized Birnbaum-Saunders distribution family introduced in [Diaz-Garcia, J.A., Leiva-Sanchez, V., 2005. A new family of life distributions based on the contoured elliptically distributions. Journal of Statistical Planning and Inference 128 (2), 445-457] with a view to make it even more flexible in terms of its kurtosis coefficient. Properties involving moments and asymmetry and kurtosis indexes are studied for some special members of this family such as the slash Birnbaum-Saunders and slash-t Birnbaum-Saunders. Simulation studies for some particular cases and a real data analysis are also reported, illustrating the usefulness of the extension considered. (C) 2008 Elsevier B.V. All rights reserved.

Bimodal extension based on the skew-normal distribution with application to pollen data

This paper considers an extension to the skew-normal model through the inclusion of an additional parameter which can lead to both uni- and bi-modal distributions. The paper presents various basic properties of this family of distributions and provides a stochastic representation which is useful for obtaining theoretical properties and to simulate from the distribution. Moreover, the singularity of the Fisher information matrix is investigated and maximum likelihood estimation for a random sample with no covariates is considered. The main motivation is thus to avoid using mixtures in fitting bimodal data as these are well known to be complicated to deal with, particularly because of identifiability problems. Data-based illustrations show that such model can be useful. Copyright (C) 2009 John Wiley & Sons, Ltd.

Epsilon Birnbaum-Saunders distribution family: properties and inference

In this paper we introduce a new extension for the Birnbaum-Saunder distribution based on the family of the epsilon-skew-symmetric distributions studied in Arellano-Valle et al. (J Stat Plan Inference 128(2):427-443, 2005). The extension allows generating Birnbaun-Saunders type distributions able to deal with extreme or outlying observations (Dupuis and Mills, IEEE Trans Reliab 47:88-95, 1998). Basic properties such as moments and Fisher information matrix are also studied. Results of a real data application are reported illustrating good fitting properties of the proposed model.

Testing hypotheses in the Birnbaum-Saunders distribution under type-II censored samples

The two-parameter Birnbaum-Saunders distribution has been used successfully to model fatigue failure times. Although censoring is typical in reliability and survival studies, little work has been published on the analysis of censored data for this distribution. In this paper, we address the issue of performing testing inference on the two parameters of the Birnbaum-Saunders distribution under type-II right censored samples. The likelihood ratio statistic and a recently proposed statistic, the gradient statistic, provide a convenient framework for statistical inference in such a case, since they do not require to obtain, estimate or invert an information matrix, which is an advantage in problems involving censored data. An extensive Monte Carlo simulation study is carried out in order to investigate and compare the finite sample performance of the likelihood ratio and the gradient tests. Our numerical results show evidence that the gradient test should be preferred. Further, we also consider the generalized Birnbaum-Saunders distribution under type-II right censored samples and present some Monte Carlo simulations for testing the parameters in this class of models using the likelihood ratio and gradient tests. Three empirical applications are presented. (C) 2011 Elsevier B.V. All rights reserved.

Life-history, thallus ontogeny, and the effects of temperature, irradiance and salinity on growth of the edible green seaweed Gayralia spp. (Chlorophyta) from Southern Brazil

Gayralia K.L. Vinogr. is a monostromatic green alga of commercial importance in the southern Brazil, and its cultivation is being considered. This paper reports some basic aspects of the biology of this poorly known genus. Two populations of Gayralia spp., from outer and inner sectors of Paranagua Bay, showed an asexual life history with a distinct pattern of thallus ontogeny. In one population (Gayralia sp. 1), zooids developed an expanded monostromatic blade directly, while in the other (Gayralia sp. 2) zooids produced an intermediate saccate stage, before giving rise to a monostromatic blade. Thalli of the two species differ in size and in cell diameter. The effects of temperature (16-30 degrees C), irradiance (50-100 mu mol photons m(-2) s(-1)), and salinity (5-40 psu) on the growth of both populations were assessed. Plantlets of Gayralia sp. 1 from in vitro cultures showed a broader tolerance to all salinity and irradiance levels tested, with the highest growth rate (GR; mean 17% day-1) at 21.5 degrees C and 100 mu mol photons m(-2) s(-1). Plantlets of Gayralia sp. 1 collected during the winter in the field showed higher GR, ranging from 5% day(-1) to 7.5% day(-1) in salinities from 20 to 40 psu, and 2.0% day(-1) and 4.3% day(-1) for plantlets collected during the summer. Gayralia sp. 2 from the field showed highest GR at salinity of 15 psu. These results suggest distinct physiological responses of the two species, in accordance with their distribution: Gayralia sp. 2 is limited to the inner areas of the estuary, while Gayralia sp. 1 grows in outer areas, where salinity values are higher than 20 psu. These data indicate that Gayralia sp. 1 has a higher potential for aquaculture than Gayralia sp. 2 due to its larger thalli, higher GR, and wider tolerance to environmental variations.

Notes on distribution, variation and characterization of Erythrolamprus pseudocorallus Roze, 1959 (Serpentes: Colubridae) with the first records from Colombia

The Maracaibo false coral snake Erythrolamprus pseudocorallus, previously known only from Venezuela, is recorded from five departments in Colombia. These new data include the westernmost and the southernmost records presently known for the species. Two specimens previously identified as E. aesculapii, from the localities of El Valle, Distrito Federal, Venezuela, and Yarumal, Antioquia, Colombia, are now attributed to E. pseudocorallus, the first one representing the northeasternmost record of the species. Morphological characterization of E. pseudocorallus is expanded based on the new specimens.

Rod bipolar cells in the retina of the capuchin monkey (Cebus apella): Characterization and distribution

Rod bipolar cells in Cebus apella monkey retina were identified by an antibody against the alpha isoform of protein kinase C (PKC alpha). which has been shown to selectively identify rod bipolars in two other primates and various mammals. Vertical sections were used to confirm the identity of these cells by their characteristic morphology of dendrites and axons. Their topographic distribution was assessed in horizontal sections; counts taken along the dorsal, ventral, nasal, and temporal quadrants. The density of rod bipolar cells increased from 500 to 2900 cells/mm(2) at 1 mm from the fovea to reach a peak of 10,000-12,000 cellss/mm(2) at 4 mm, approximately 5 deg of eccentricity, and then gradually decreased toward retinal periphery to values of 5000 cells/mm(2) or less. Rod to rod bipolar density ratio remained between 10 and 20 across most of the retinal extension. The number of rod bipolar cells per retina was 6,360,000 +/- 387,433 (mean +/- S.D., n = 6). The anti-PKC alpha antibody has shown to be a good marker of rod bipolar cells of Cebus, and the cell distribution is similar to that described for other primates. In spite of the difference in the central retina, the density variation of rod bipolar cells in the Cebus and Macaca as well as the convergence from rod to rod bipolar cells are Generally similar, suggesting that both retinae stabilize similar sensitivity (as measured by rod density) and convergence.

Bayesian analysis for a skew extension of the multivariate null intercept measurement error model

Skew-normal distribution is a class of distributions that includes the normal distributions as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis in a multivariate, null intercept, measurement error model [R. Aoki, H. Bolfarine, J.A. Achcar, and D. Leao Pinto Jr, Bayesian analysis of a multivariate null intercept error-in -variables regression model, J. Biopharm. Stat. 13(4) (2003b), pp. 763-771] where the unobserved value of the covariate (latent variable) follows a skew-normal distribution. The results and methods are applied to a real dental clinical trial presented in [A. Hadgu and G. Koch, Application of generalized estimating equations to a dental randomized clinical trial, J. Biopharm. Stat. 9 (1999), pp. 161-178].