Some characterizations of multivariate distributions using products of the hazard gradient and mean residual life components

We give a general procedure to characterize multivariate distributions by using products of the hazard gradient and mean residual life components. This procedure is applied to characterize multivariate distributions as Gumbel exponential, Lomax, Burr, Pareto and generalized Pareto multivariate distributions. Our results extend the results of several authors and can be used to study how to extend univariate models to the multivariate set-up.     

A very simple proof of the multivariate Chebyshev's inequality

Abstract

In this short note, a very simple proof of the Chebyshev's inequality for random vectors is given. This inequality provides a lower bound for the percentage of the population of an arbitrary random vector X with finite mean μ = E(X) and a positive definite covariance matrix V = Cov(X) whose Mahalanobis distance with respect to V to the mean μ is less than a fixed value. The main advantage of the proof is that it is a simple exercise for a first year probability course. An alternative proof based on principal components is also provided. This proof can be used to study the case of a singular covariance matrix V.     

Comparisons of coherent systems with non-identically distributed components

The signature-based mixture representations for coherent systems are a good way to obtain distribution-free comparisons of systems. Unfortunately, these representations only hold for systems whose component lifetimes are independent and identically distributed (IID) or exchangeable (i.e., their joint distribution is invariant under permutations). In this paper we obtain comparison results for generalized mixtures, that is, for reliability functions that can be written as linear combinations of some baseline reliability functions with positive and negative coefficients. These results are based on some concepts in Graph Theory. We apply these results to obtain new comparison results for coherent systems without the IID or exchangeability assumptions by using their generalized mixture representations based on the minimal path sets.     

Statistical analysis of data from dilution assays with censored correlated counts

Frequently, count data obtained from dilution assays are subject to an upper detection limit, and as such, data obtained from these assays are usually censored. Also, counts from the same subject at different dilution levels are correlated. Ignoring the censoring and the correlation may provide unreliable and misleading results. Therefore, any meaningful data modeling requires that the censoring and the correlation be simultaneously addressed. Such comprehensive approaches of modeling censoring and correlation are not widely used in the analysis of dilution assays data. Traditionally, these data are analyzed using a general linear model on a logarithmic-transformed average count per subject. However, this traditional approach ignores the between-subject variability and risks, providing inconsistent results and unreliable conclusions. In this paper, we propose the use of a censored negative binomial model with normal random effects to analyze such data. This model addresses, in addition to the censoring and the correlation, any overdispersion that may be present in count data. The model is shown to be widely accessible through the use of several modern statistical software.     

Testing the Personal Wellbeing Index on 12–16?Year-Old Adolescents in 3 Different Countries with 2 New Items

The 7-item adult version of the Personal Wellbeing scale (Cummins et al. Social Indic Res 64:159?C190, 2003) was administered to two samples of adolescents aged 12?C16 in Brazil (N?=?1,588) and Spain (N?=?2,900), and to a sample of adolescents aged 14?C16 in Chile (N?=?843). The results obtained were analyzed to determine its psychometric characteristics when used with adolescents in the three different countries and to check whether two additional items would improve its qualities. Results reveal that the new PWI-9 version worked well with the adolescents in the three countries, improving some of the qualities of the PWI-7. One of the added items, satisfaction with oneself, appears to be a major contributor to unique explained variance when regressed on the single-item of overall life satisfaction (OLS). The model we present using structural equations shows good fit statistics for the factor structure, with both 7 and 9 items. Separate in-country analyses demonstrate that cultural context has a strong influence on correlations and saturations between the studied variables and also on the explained variance. Probably related to this fact, the Model fit structure is good in Brazil (with a low PWI variance accounted for by its predictors) and Spain (medium), but rather modest in Chile, where data show a high proportion of the PWI variance accounted for by its predictors. However, a multi-group factor analysis among the three countries restricting saturations to 1 in each country in order to make data comparable across countries still show a good fit of the proposed model for both PWI-7 and PWI-9.     

The impact of key success factors on company performance

This article presents the results of a large scale survey taken among U.S. manufacturers of mature industrial products. The results of the study indicated that within each product/market there are some tasks which are more important (i.e. critical) than others for success—success being defined as outperforming the competition in terms of profitability. The results also showed that different product/market areas have different critical success factors, but the more similar they are in their make-up the more similar their key success factors tend to be.     

On the performance of two clustering methods for spatial functional data

The performance of two clustering strategies for spatially correlated functional data based on the same measure of spatial dependence is examined and compared. In particular, the role of the spatial dependence computed by the trace-variogram function is analyzed. The main features of both procedures is shown through a simulation study based on a variety of practical scenarios easily encountered in the analysis of spatial functional data. An application on real data based on salinity curves is also presented.     

Use of exponential power distributions for mixture models in the presence of covariates

In this paper, we present a Bayesian analysis of exponential power mixture models in the presence of a covariate. Considering Gibbs sampling with MetropolisHastings algorithms, we obtain Monte Carlo estimates for the posterior quantities of interest.     

Sensitivity analysis and choosing between alternative polytomous IRT models using Bayesian model comparison criteria

Polytomous Item Response Theory (IRT) models are used by specialists to score assessments and questionnaires that have items with multiple response categories. In this article, we study the performance of five model comparison criteria for comparing fit of the graded response and generalized partial credit models using the same dataset when the choice between the two is unclear. Simulation study is conducted to analyze the sensitivity of priors and compare the performance of the criteria using the No-U-Turn Sampler algorithm, under a Bayesian approach. The results were used to select a model for an application in mental health data.     

How to Do Things With Texts: A Functional Account of Reading Comprehension

We offer an account of reading comprehension that we believe will help clarify some common conceptual confusions in the relevant literature, as well as contribute to existing functional accounts. We argue that defining texts qua texts as stimulus classes, on the one hand, and equating “comprehension” with behavior (covert or otherwise), on the other, are not useful conceptual moves, especially when behavioral settings go beyond basic literacy skills acquisition. We then analyze the structure of the contingencies that usually evoke talk of “comprehension” using techniques from analytic philosophy. We show how keeping the results of this analysis in mind can help avoid the conceptual bafflement that often arises, even among behavior analysts, when defining or assessing behavioral phenomena related to reading comprehension. Using two contrasting cases (legal texts and stories), we argue that what counts as comprehension depends, not peripherally but crucially, on the shared social practices of which texts are a part. Finally, we propose a new framework for classifying reader–text contingencies by combining two dimensions: openness of setting and embeddedness of reinforcement.