On the Skew-Normal-Cauchy Distribution

In this article, we study further properties of a skew normal distribution, called the skew-normal-Cauchy (SNC) distribution by Nadarajah and Kotz (2003). A stochastic representation is obtained which allows alternative derivations for moments, moments generating function, and skewness and kurtosis coefficients. Issues related to singularity of the Fisher information matrix are investigated.

Local Influence Analysis for Skew-Normal Linear Mixed Models

In this article, we consider local influence analysis for the skew-normal linear mixed model (SN-LMM). As the observed data log-likelihood associated with the SN-LMM is intractable, Cook`s well-known approach cannot be applied to obtain measures of local influence. Instead, we develop local influence measures following the approach of Zhu and Lee (2001). This approach is based on the use of an EM-type algorithm and is measurement invariant under reparametrizations. Four specific perturbation schemes are discussed. Results obtained for a simulated data set and a real data set are reported, illustrating the usefulness of the proposed methodology.

The best are never normal : exploring the distribution of firm performance

Competitive Strategy literature predicts three different mechanisms of performance generation, thus distinguishing between firms that have competitive advantage, firms that have competitive disadvantage or firms that have neither. Nonetheless, previous works in the field have fitted a single normal distribution to model firm performance. Here, we develop a new approach that distinguishes among performance generating mechanisms and allows the identification of firms with competitive advantage or disadvantage. Theorizing on the positive feedback loops by which firms with competitive advantage have facilitated access to acquire new resources, we proposed a distribution we believe data on firm performance should follow. We illustrate our model by assessing its fit to data on firm performance, addressing its theoretical implications and comparing it to previous works.

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.

Size frequency distribution of prion protein (PrP) aggregates in variant Creutzfeldt-Jakob disease (vCJD)

The frequency distribution of aggregate size of the diffuse and florid-type prion protein (PrP) plaques was studied in various brain regions in cases of variant Creutzfeldt-Jakob disease (vCJD). The size distributions were unimodal and positively skewed and resembled those of β-amyloid (Aβ) deposits in Alzheimer's disease (AD) and Down's syndrome (DS). The frequency distributions of the PrP aggregates were log-normal in shape, but there were deviations from the expected number of plaques in specific size classes. More diffuse plaques were observed in the modal size class and fewer in the larger size classes than expected and more florid plaques were present in the larger size classes compared with the log-normal model. It was concluded that the growth of the PrP aggregates in vCJD does not strictly follow a log-normal model, diffuse plaques growing to within a more restricted size range and florid plaques to larger sizes than predicted. © Springer-Verlag 2005.