Construction of bivariate and multivariate weighted distributions via conditioning

Weighted distributions (univariate and bivariate) have received widespread attention over the last two decades because of their flexibility for analyzing skewed data. In this article, we propose an alternative method to construct a new family of bivariate and multivariate weighted distributions. For illustrative purposes, some examples of the proposed method are presented. Several structural properties of the bivariate weighted distributions including marginal distributions together with distributions of the minimum and maximum, evaluation of the reliability parameter, and verification of total positivity of order two are also presented. In addition, we provide some multivariate extensions of the proposed models. A real-life data set is used to show the applicability of these bivariate weighted distributions.     

Some alternative bivariate Kumaraswamy models

In this article we discuss various strategies for constructing bivariate Kumaraswamy distributions. As alternatives to the Nadarajah et al. (2011) bivariate model, four different models are introduced utilizing a conditional specification approach, a conditional survival function approach, and an Arnold–Ng bivariate beta distribution construction approach. Distributional properties for such bivariate distributions are investigated. Parameter estimation strategies for the models are discussed, as are the consequences of fitting two of the models to a particular data set involving the proportion of foggy days at two different airports in Colombia.     

Psychometric and Demographic Predictors of the Perceived Risk of Terrorist Threats and the Willingness to Pay for Terrorism Risk Management Programs

A 2009 national telephone survey of 924 U.S. adults assessed perceptions of terrorism and homeland security issues. Respondents rated severity of effects, level of understanding, number affected, and likelihood of four terrorist threats: poisoned water supply; explosion of a small nuclear device in a major U.S. city; an airplane attack similar to 9/11; and explosion of a bomb in a building, train, subway, or highway. Respondents rated perceived risk and willingness to pay (WTP) for dealing with each threat. Demographic, attitudinal, and party affiliation data were collected. Respondents rated bomb as highest in perceived risk but gave the highest WTP ratings to nuclear device. For both perceived risk and WTP, psychometric variables were far stronger predictors than were demographic ones. OLS regression analyses using both types of variables to predict perceived risk found only two significant demographic predictors for any threat—Democrat (a negative predictor for bomb) and white male (a significant positive predictor for airline attack). In contrast, among psychometric variables, severity, number affected, and likelihood were predictors of all four threats and level of understanding was a predictor for one. For WTP, education was a negative predictor for three threats; no other demographic variables were significant predictors for any threat. Among psychometric variables, perceived risk and number affected were positive predictors of WTP for all four threats; severity and likelihood were predictors for three; level of understanding was a significant predictor for two.     

Optimal Information Processing and Bayes's Theorem

In this article statistical inference is viewed as information processing involving input information and output information. After introducing information measures for the input and output information, an information criterion functional is formulated and optimized to obtain an optimal information processing rule (IPR). For the particular information measures and criterion functional adopted, it is shown that Bayes's theorem is the optimal IPR. This optimal IPR is shown to be 100% efficient in the sense that its use leads to the output information being exactly equal to the given input information. Also, the analysis links Bayes's theorem to maximum-entropy considerations.     

Self-employment and economic leadership as two promising perspectives on rural disability and work

A defining difference between rural and urban circumstances for people with disabilities involves opportunities for work. One of the most significant elements of the rural context is that economic conditions in rural communities consistently trail the national economy. This paper presents an overview of disability in rural America and outlines an ecological model for guiding the development of rural solutions to rehabilitation problems. Two promising examples of such solutions, self-employment as a rural vocational rehabilitation employment option and rural economic leadership by people with disabilities, are outlined.