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.

Improved likelihood inference in beta regression

We consider the issue of performing accurate small-sample likelihood-based inference in beta regression models, which are useful for modelling continuous proportions that are affected by independent variables. We derive small-sample adjustments to the likelihood ratio statistic in this class of models. The adjusted statistics can be easily implemented from standard statistical software. We present Monte Carlo simulations showing that inference based on the adjusted statistics we propose is much more reliable than that based on the usual likelihood ratio statistic. A real data example is presented.

Bayesian inference for a skew-normal IRT model under the centred parameterization

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is interest in studying latent variables. These latent variables are directly considered in the Item Response Models (IRM) and they are usually called latent traits. A usual assumption for parameter estimation of the IRM, considering one group of examinees, is to assume that the latent traits are random variables which follow a standard normal distribution. However, many works suggest that this assumption does not apply in many cases. Furthermore, when this assumption does not hold, the parameter estimates tend to be biased and misleading inference can be obtained. Therefore, it is important to model the distribution of the latent traits properly. In this paper we present an alternative latent traits modeling based on the so-called skew-normal distribution; see Genton (2004). We used the centred parameterization, which was proposed by Azzalini (1985). This approach ensures the model identifiability as pointed out by Azevedo et al. (2009b). Also, a Metropolis Hastings within Gibbs sampling (MHWGS) algorithm was built for parameter estimation by using an augmented data approach. A simulation study was performed in order to assess the parameter recovery in the proposed model and the estimation method, and the effect of the asymmetry level of the latent traits distribution on the parameter estimation. Also, a comparison of our approach with other estimation methods (which consider the assumption of symmetric normality for the latent traits distribution) was considered. The results indicated that our proposed algorithm recovers properly all parameters. Specifically, the greater the asymmetry level, the better the performance of our approach compared with other approaches, mainly in the presence of small sample sizes (number of examinees). Furthermore, we analyzed a real data set which presents indication of asymmetry concerning the latent traits distribution. The results obtained by using our approach confirmed the presence of strong negative asymmetry of the latent traits distribution. (C) 2010 Elsevier B.V. All rights reserved.

Inference for a skew extension of the Grubbs model

In this paper, we discuss inferential aspects for the Grubbs model when the unknown quantity x (latent response) follows a skew-normal distribution, extending early results given in Arellano-Valle et al. (J Multivar Anal 96:265-281, 2005b). Maximum likelihood parameter estimates are computed via the EM-algorithm. Wald and likelihood ratio type statistics are used for hypothesis testing and we explain the apparent failure of the Wald statistics in detecting skewness via the profile likelihood function. The results and methods developed in this paper are illustrated with a numerical example.

Improved likelihood inference in Birnbaum-Saunders regressions

The Birnbaum-Saunders regression model is commonly used in reliability studies. We address the issue of performing inference in this class of models when the number of observations is small. Our simulation results suggest that the likelihood ratio test tends to be liberal when the sample size is small. We obtain a correction factor which reduces the size distortion of the test. Also, we consider a parametric bootstrap scheme to obtain improved critical values and improved p-values for the likelihood ratio test. The numerical results show that the modified tests are more reliable in finite samples than the usual likelihood ratio test. We also present an empirical application. (C) 2009 Elsevier B.V. All rights reserved.

Properties and Inference on the Skew-Curved-Symmetric Family of Distributions

In this article, we study some results related to a specific class of distributions, called skew-curved-symmetric family of distributions that depends on a parameter controlling the skewness and kurtosis at the same time. Special elements of this family which are studied include symmetric and well-known asymmetric distributions. General results are given for the score function and the observed information matrix. It is shown that the observed information matrix is always singular for some special cases. We illustrate the flexibility of this class of distributions with an application to a real dataset on characteristics of Australian athletes.

Improved testing inference in mixed linear models

Mixed linear models are commonly used in repeated measures studies. They account for the dependence amongst observations obtained from the same experimental unit. Often, the number of observations is small, and it is thus important to use inference strategies that incorporate small sample corrections. In this paper, we develop modified versions of the likelihood ratio test for fixed effects inference in mixed linear models. In particular, we derive a Bartlett correction to such a test, and also to a test obtained from a modified profile likelihood function. Our results generalize those in [Zucker, D.M., Lieberman, O., Manor, O., 2000. Improved small sample inference in the mixed linear model: Bartlett correction and adjusted likelihood. Journal of the Royal Statistical Society B, 62,827-838] by allowing the parameter of interest to be vector-valued. Additionally, our Bartlett corrections allow for random effects nonlinear covariance matrix structure. We report simulation results which show that the proposed tests display superior finite sample behavior relative to the standard likelihood ratio test. An application is also presented and discussed. (C) 2008 Elsevier B.V. All rights reserved.

FROM TRISECTIONS IN MODULE CATEGORIES TO QUASI-DIRECTED COMPONENTS

In this paper, we define and study a special type of trisections in a module category, namely the compact trisections which characterize quasi-directed components. We apply this notion to the study of laura algebras and we use it to define a class of algebras with predictable Auslander-Reiten components.

Experimental performance of a string module in a CPC reflector cavity

The purpose of the work is to develop a cost effective semistationary CPC concentrator for a string PV-module. A novel method of using annual irradiation distribution diagram projected in a north-south vertical plane is developed. This method allows us easily to determine the optimum acceptance angle of the concentrator and the required number of annual tilts. Concentration ranges of 2-5x are investigated with corresponding acceptance angles between 5 and 15°. The concentrator should be tilted 2-6 times per year. Experiments has been performed on a string module of 10 cells connected in a series and equipped with a compound parabolic concentrator with C = 3.3X. Measurement show that the output will increase with a factor of 2-2.5 for the concentrator module, compared to a reference module without concentrator. If very cheap aluminium reflectors are used the costs for the PV-module can be decreased nearly by a factor of two.

Residual-based Inference for Common Nonlinear Features

This paper investigates common nonlinear features in multivariate nonlinear autore-gressive models via testing the estimated residuals. A Wald-type test is proposed and itis asymptotically Chi-squared distributed. Simulation studies are given to examine thefinite-sample properties of the proposed test.

Module property verification : A method to plan and perform quality verifications in modular architectures

Modular product architectures have generated numerous benefits for companies in terms of cost, lead-time and quality. The defined interfaces and the module’s properties decrease the effort to develop new product variants, and provide an opportunity to perform parallel tasks in design, manufacturing and assembly. The background of this thesis is that companies perform verifications (tests, inspections and controls) of products late, when most of the parts have been assembled. This extends the lead-time to delivery and ruins benefits from a modular product architecture; specifically when the verifications are extensive and the frequency of detected defects is high. Due to the number of product variants obtained from the modular product architecture, verifications must handle a wide range of equipment, instructions and goal values to ensure that high quality products can be delivered. As a result, the total benefits from a modular product architecture are difficult to achieve. This thesis describes a method for planning and performing verifications within a modular product architecture. The method supports companies by utilizing the defined modules for verifications already at module level, so called MPV (Module Property Verification). With MPV, defects are detected at an earlier point, compared to verification of a complete product, and the number of verifications is decreased. The MPV method is built up of three phases. In Phase A, candidate modules are evaluated on the basis of costs and lead-time of the verifications and the repair of defects. An MPV-index is obtained which quantifies the module and indicates if the module should be verified at product level or by MPV. In Phase B, the interface interaction between the modules is evaluated, as well as the distribution of properties among the modules. The purpose is to evaluate the extent to which supplementary verifications at product level is needed. Phase C supports a selection of the final verification strategy. The cost and lead-time for the supplementary verifications are considered together with the results from Phase A and B. The MPV method is based on a set of qualitative and quantitative measures and tools which provide an overview and support the achievement of cost and time efficient company specific verifications. A practical application in industry shows how the MPV method can be used, and the subsequent benefits

Beneftis of modularity and module level tests

Many companies implement a modular architecture to support the need to create more variants with less effort. Although the modular architecture has many benefits, the tests to detect any defects become a major challenge. However, a modular architecture with defined functional elements seems beneficial to test at module level, so called MPV (Module Property Verification). This paper presents studies from 29 companies with the purpose of showing trends in the occurrence of defects and how these can support the MPV.