In many applications, assumptions about the log-concavity of a probability distribution allow just enough special structure to yield a workable theory. This paper catalogs a series of theorems relating log-concavity and/or log-convexity of probability density functions, distribution functions, reliability functions, and their integrals. We list a large number of commonly-used probability distributions and report the log-concavity or log-convexity of their density functions and their integrals. We also discuss a variety of applications of log-concavity that have appeared in the literature. Copyright Springer-Verlag Berlin/Heidelberg 2005Log-concavity. Reliability, Hazard functions, Probability distributions, Failure rates, Costly appraisals, Mean residual lifetime.,
The bibliometric measure impact factor is a leading indicator of journal influence, and impact factors are routinely used in making decisions ranging from selecting journal subscriptions to allocating research funding to deciding tenure cases. Yet journal impact factors have increased gradually over time, and moreover impact factors vary widely across academic disciplines. Here we quantify inflation over time and differences across fields in impact factor scores and determine the sources of these differences. We find that the average number of citations in reference lists has increased gradually, and this is the predominant factor responsible for the inflation of impact factor scores over time. Field-specific variation in the fraction of citations to literature indexed by Thomson Scientific's Journal Citation Reports is the single greatest contributor to differences among the impact factors of journals in different fields. The growth rate of the scientific literature as a whole, and cross-field differences in net size and growth rate of individual fields, have had very little influence on impact factor inflation or on cross-field differences in impact factor.
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SARS-CoV-2 coronavirus has proven difficult to control not only because of its high transmissibility, but because those who are infected readily spread the virus before symptoms appear, and because some infected individuals, though contagious, never exhibit symptoms. Proactive testing of asymptomatic individuals is therefore a powerful, and probably necessary, tool for preventing widespread infection in many settings. This paper explores the effectiveness of alternative testing regimes, in which the frequency, the accuracy, and the delay between testing and results determine the time path of infection. For a simple model of disease transmission, we present analytic formulas that determine the effect of testing on the expected number of days of during which an infectious individual is exposed to the population at large. This allows us to estimate the frequency of testing that would be required to prevent uncontrolled outbreaks, and to explore the trade-offs between frequency, accuracy, and delay in achieving this objective. We conclude by discussing applications to outbreak control on college and university campuses.
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