The exponential distribution analog of the Grubbs–Weaver method

Abstract

Grubbs and Weaver (1947 Grubbs, F. E., and C. L. Weaver. 1947. The best unbiased estimate of population standard deviation based on group ranges. Journal of the American Statistical Association 42 (238):224–41. doi: 10.2307/2280652.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) suggest a minimum-variance unbiased estimator for the population standard deviation of a normal random variable, where a random sample is drawn and a weighted sum of the ranges of subsamples is calculated. The optimal choice involves using as many subsamples of size eight as possible. They verified their results numerically for samples of size up to 100, and conjectured that their “rule of eights” is valid for all sample sizes. Here we examine the analogous problem where the underlying distribution is exponential and find that a “rule of fours” yields optimality and prove the result rigorously.     

20 years of Bologna - a story of success,a story of failure

The Bologna Process is a unique harmonisation process taking place outside the policy-making framework of the European Union. It aims at enhancing the comparability and compatibility of higher education structures and degrees across Europe, as well as to institutionalise quality assurance mechanisms. The aim of this article is to provide a condensed, up-to-date overview of the Bologna Process with regard to structural characteristics, before embedding it into a discussion on processes on voluntary policy convergence and to which extent we should be able to find this kind of policy harmonisation in the realm of the Bologna Process. Related to this are questions why this, in principle, completely voluntary process of policy harmonisation, has appealed to so many countries and why they might or might not feel committed to the implementation of its policies and tools.     

The (Conditional) Resource Dilution Model: State- and Community-Level Modifications

Demography - One of the most consistent patterns in the social sciences is the relationship between sibship size and educational outcomes: those with fewer siblings outperform those with many. The...     

USING THE PARETO DISTRIBUTION TO IMPROVE ESTIMATES OF TOPCODED EARNINGS

Inconsistent censoring in the public‐use March Current Population Survey (CPS) limits its usefulness in measuring labor earnings trends, as previous approaches for imputing topcoded earnings systematically understate top earnings. Using Pareto estimation methods with less‐censored internal data, we create an enhanced cell‐mean series to capture top earnings in the public‐use data. Annual earnings inequality trends since 1963 using our series largely mirror those found by Kopczuk, Saez, and Song using social security administration data for commerce and industry workers. When we extend our analysis to 2013 and consider all workers, earnings inequality levels are higher but its growth is more modest. (JEL C81, D31, J01)     

Predictive Hierarchic Modeling of Operational Characteristics in Clinical Trials

An analytic methodology for patient enrollment modeling using a Poisson-gamma model is developed by Anisimov & Fedorov (2005–2007). For modeling hierarchic processes associated with enrollment, a new methodology using evolving stochastic processes is proposed. This provides rather general and unified framework to describe various operational processes associated with enrollment. The technique for calculating predictive distributions, mean, and credibility bounds for evolving processes is developed. Some applications to modeling operational characteristics in clinical trials are considered with focus to modeling events associated with incoming and follow-up patients in different settings. For these models, predictive characteristics are derived in a closed form.     

Analysis of California propositions: An experiment in the empirical revelation of shared mental models

This paper uses factor analysis to analyze Californians’ voting on 12 propositions considered during the 2008 general election. The result is to create quantitative representations of shared mental models. After generating two county-level shared mental model indices, the indices are further examined to explain their variation across counties and to evaluated their performance as substitutes for previous presidential voting as an independent variable in a presidential voting model.     

Mobility and Professional Networks in Academia: An Exploration of the Obligations of Presence

This article explores the obligations of presence behind work-related mobility for academics in internationalizing higher education systems. By further developing John Urry’s concept of ‘meetingness’, the article reveals how academics depend on corporeal and virtual mobility to create and maintain a networked professional life outside their own institution, which is crucial in the context of changing work conditions. Our insights are drawn from original qualitative research (42 interviews) in a Flemish and Danish context. The data reveal obligations of presence associated with an interrelated mix of functionality, and the construction of dense and sparse social networks that together support career success and work at the frontiers of academic knowledge. Despite the now well-recognized costs of corporeal mobility, obligations of presence result in virtual and corporeal mobility coexisting, rather than the former substituting for the latter. Virtual mobility is mainly used when conflicting obligations of presence exist, and as a means of sustaining networks over time given the processual nature of meetingness, rather than as a means to reduce levels of corporeal mobility.     

Applications of quadrivariate exponential distribution to a three-unit warm standby system with dependent structure

Two-unit warm standby systems have been elaborately dealt within the literature. However, the study of standby systems with more than two units, though very relevant in state-of-the-art practical situations, has received little attention because of mathematical intricacies involved in analyzing them. Also, such systems have been studied assuming: (i) the lifetime or repair time of the units to be exponential, or (ii) the lifetime and repair time to be independent. The present contribution is an improvement in the state-of-the-art in the sense that three-unit warm standby system with dependent structure is shown to be capable of comprehensive analysis.     

Housing hardship and energy insecurity among native-born and immigrant low-income families with children in the United States

The costs for rent and utilities account for the largest share of living expenses, yet these two critical dimensions of material hardship have seldom been examined concurrently in population-based studies. This paper employs multivariate statistical analysis using American Community Survey data to demonstrate the relative risk ratio of low-income renter-occupied households with children experiencing ‘rent burden', ‘energy insecurity', or a ‘double burden’ as opposed to no burden. Findings suggest that low-income households are more likely to experience these economic hardships in general but that specific groups are disproportionately burdened in different ways. For instance, whereas immigrants are more likely to experience rental burden, they are less likely to experience energy insecurity and are also spared from the double burden. In contrast, native-born African Americans are more likely than all other groups to experience the double burden. These results may be driven by the housing stock available to certain groups due to racial residential segregation, decisions regarding the quality of housing low-income householders are able to afford, as well as home-country values, such as modest living and energy conservation practices, among immigrant families. This paper also points to important policy gaps in safety net benefits related to housing and energy targeting low-income households.