Shared information in stationary states at criticality

We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the information shared between the two subsystems. If the correlation length is finite, the estimators stay finite for large system sizes. If the correlation length diverges, so do the estimators. The definition of the estimators is inspired by information theory. We look at several models and compare the behaviors of the estimators in the finite-size scaling limit. Analytical and numerical methods as well as Monte Carlo simulations are used. We show how the finite-size scaling functions change for various phase transitions, including the case where one has conformal invariance.

Femtosecond light distribution at skin and liver of rats: analysis for use in optical diagnostics

In this study we investigated the light distribution under femtosecond laser illumination and its correlation with the collected diffuse scattering at the surface of ex-vivo rat skin and liver. The reduced scattering coefficients mu`s for liver and skin due to different scatterers have been determined with Mie-scattering theory for each wavelength (800, 630, and 490 nm). Absorption coefficients mu(a) were determined by diffusion approximation equation in correlation with measured diffused reflectance experimentally for each wavelength (800, 630, and 490 nm). The total attenuation coefficient for each wavelength and type of tissue were determined by linearly fitting the log based normalized intensity. Both tissues are strongly scattering thick tissues. Our results may be relevant when considering the use of femtosecond laser illumination as an optical diagnostic tool. [GRAPHICS] A typical sample of skin exposed to 630 nm laser light (C) 2010 by Astro Ltd. Published exclusively by WILEY-VCH Verlag GmbH & Co. KGaA

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.

Improved score tests in symmetric linear regression models

The class of symmetric linear regression models has the normal linear regression model as a special case and includes several models that assume that the errors follow a symmetric distribution with longer-than-normal tails. An important member of this class is the t linear regression model, which is commonly used as an alternative to the usual normal regression model when the data contain extreme or outlying observations. In this article, we develop second-order asymptotic theory for score tests in this class of models. We obtain Bartlett-corrected score statistics for testing hypotheses on the regression and the dispersion parameters. The corrected statistics have chi-squared distributions with errors of order O(n(-3/2)), n being the sample size. The corrections represent an improvement over the corresponding original Rao`s score statistics, which are chi-squared distributed up to errors of order O(n(-1)). Simulation results show that the corrected score tests perform much better than their uncorrected counterparts in samples of small or moderate size.

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.

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.

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.

Multivariate measurement error models based on scale mixtures of the skew-normal distribution

Scale mixtures of the skew-normal (SMSN) distribution is a class of asymmetric thick-tailed distributions that includes the skew-normal (SN) distribution as a special case. The main advantage of these classes of distributions is that they are easy to simulate and have a nice hierarchical representation facilitating easy implementation of the expectation-maximization algorithm for the maximum-likelihood estimation. In this paper, we assume an SMSN distribution for the unobserved value of the covariates and a symmetric scale mixtures of the normal distribution for the error term of the model. This provides a robust alternative to parameter estimation in multivariate measurement error models. Specific distributions examined include univariate and multivariate versions of the SN, skew-t, skew-slash and skew-contaminated normal distributions. The results and methods are applied to a real data set.

Framework for Skew-Probit Links in Binary Regression

We review several asymmetrical links for binary regression models and present a unified approach for two skew-probit links proposed in the literature. Moreover, under skew-probit link, conditions for the existence of the ML estimators and the posterior distribution under improper priors are established. The framework proposed here considers two sets of latent variables which are helpful to implement the Bayesian MCMC approach. A simulation study to criteria for models comparison is conducted and two applications are made. Using different Bayesian criteria we show that, for these data sets, the skew-probit links are better than alternative links proposed in the literature.

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.

A reparametrization of Triangular Distribution based on the Skew-Symmetric Distributions

In this paper a new approach is considered for studying the triangular distribution using the theoretical development behind Skew distributions. Triangular distribution are obtained by a reparametrization of usual triangular distribution. Main probabilistic properties of the distribution are studied, including moments, asymmetry and kurtosis coefficients, and an stochastic representation, which provides a simple and efficient method for generating random variables. Moments estimation is also implemented. Finally, a simulation study is conducted to illustrate the behavior of the estimation approach proposed.

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.

On estimation and influence diagnostics for the Grubbs` model under heavy-tailed distributions

The Grubbs` measurement model is frequently used to compare several measuring devices. It is common to assume that the random terms have a normal distribution. However, such assumption makes the inference vulnerable to outlying observations, whereas scale mixtures of normal distributions have been an interesting alternative to produce robust estimates, keeping the elegancy and simplicity of the maximum likelihood theory. The aim of this paper is to develop an EM-type algorithm for the parameter estimation, and to use the local influence method to assess the robustness aspects of these parameter estimates under some usual perturbation schemes, In order to identify outliers and to criticize the model building we use the local influence procedure in a Study to compare the precision of several thermocouples. (C) 2008 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.