Our aim is to model the frequency of certain behavioral acts, especially those that are likely to transmit communicable diseases between persons. We develop a generalized linear model based on the beta prime distribution to model the responses to a survey question of the form, “When was the last time that you engaged in this behavior?” Intuitively, individuals reporting more recent events are more likely to have greater frequency of the risky behavior. The beta prime distribution is especially suited to this application because of its long tail. We adjust for length-biased sampling. We show how to use this distribution as the basis of a linear regression model that accounts for differences in demographic and psychological characteristics of the respondents. We discuss estimation of parameters, residuals, tests for heterogeneity of these parameters, and jackknife measures of influence. The methods are applied to a survey of alcohol abuse use among individuals who are at high risk for spreading HIV and other communicable diseases in a study conducted in St. Petersburg, Russia.
Abstract. Civil engineering is a branch of science that covers a broad range of areas where experimental procedures often plays an important role. The research in this field is usually supported by experimental structures able to test physical and mathematical models and to provide measurement results with acceptable accuracy. To assure measurement quality, a metrology probabilistic approach can provide valuable mathematical and computational tools especially suited to the study, evaluation and improvement of measurement processes in its different components (modeling, instrumentation performance, data processing, data validation and traceability), emphasizing measurement uncertainty evaluation as a tool to the analysis of results and to promote the quality and capacity associated with decision-making. This paper presents some of the research held by the metrology division of the Portuguese civil engineering research institutes, focused on the contribution of measurement uncertainty studies to a variety of frameworks, such as testing for metrological characterization and physical and mathematical modeling. Experimental data will be used to illustrate practical cases.
Abstr act. The evaluation of measurement uncertainty, in certain fields of science, faces the problem of scarcity of data. This is certainly the case in the testing of geological soils in civil engineering, where tests can take several days or weeks and where the same sample is not available for further testing, being destroyed during the experiment. In this particular study attention will be paid to triaxial compression tests used to typify particular soils. The purpose of the testing is to determine two parameters that characterize the soil, namely, cohesion and friction angle. These parameters are defined in terms of the intercept and slope of a straight line fitted to a small number of points (usually three) derived from experimental data. The use of ordinary least squares to obtain uncertainties associated with estimates of the two parameters would be unreliable if there were only three points (and no replicates) and hence only one degrees of freedom. Intr oductionThe triaxial compression test involves having the soil specimen loaded to failure, by compression, when submitted to a specified confined stress. Through a series of tests, usually three, with different confinement stresses, the required experimental data to draw the failure line (stress coordinates representing failure, see Figure 2) are obtained, from which it is possible to determine its intercept and the slope. This information is then used to determine two parameters that characterize the soil, namely, the cohesion and friction angle. The coordinate axes represent the effective normal stress and the shear stress resulting from different consolidation stresses applied to the soil specimen. The triaxial compression test is performed according to the standard CEN ISO/TEC 17892-9 [1].The study will focus on problems linked to the construction of a straight line given data from these experiments. The use of ordinary least squares to obtain uncertainties associated with estimates of the two parameters would be unreliable if there were only three points (and no replicates) and hence one degrees of freedom. These uncertainties would be more reliably obtained in terms of the uncertainties associated with estimates of quantities representing the coordinates of each point provided by measurement models for those quantities. Sometimes, however, there may be measured values available from a small number (two or possibly three) of experiments at each consolidation stress § To whom correspondence should be addressed 13th IMEKO TC1-TC7 Joint Symposium
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