The Newcomb-Benford Law in Its Relation to Some Common Distributions

An often reported, but nevertheless persistently striking observation, formalized as the Newcomb-Benford law (NBL), is that the frequencies with which the leading digits of numbers occur in a large variety of data are far away from being uniform. Most spectacular seems to be the fact that in many data the leading digit 1 occurs in nearly one third of all cases. Explanations for this uneven distribution of the leading digits were, among others, scale- and base-invariance. Little attention, however, found the interrelation between the distribution of the significant digits and the distribution of the observed variable. It is shown here by simulation that long right-tailed distributions of a random variable are compatible with the NBL, and that for distributions of the ratio of two random variables the fit generally improves. Distributions not putting most mass on small values of the random variable (e.g. symmetric distributions) fail to fit. Hence, the validity of the NBL needs the predominance of small values and, when thinking of real-world data, a majority of small entities. Analyses of data on stock prices, the areas and numbers of inhabitants of countries, and the starting page numbers of papers from a bibliography sustain this conclusion. In all, these findings may help to understand the mechanisms behind the NBL and the conditions needed for its validity. That this law is not only of scientific interest per se, but that, in addition, it has also substantial implications can be seen from those fields where it was suggested to be put into practice. These fields reach from the detection of irregularities in data (e.g. economic fraud) to optimizing the architecture of computers regarding number representation, storage, and round-off errors

Effects of Particulate Air Pollution on Cardiovascular Health: A Population Health Risk Assessment

Particulate matter (PM) air pollution is increasingly recognized as an important and modifiable risk factor for adverse health outcomes including cardiovascular disease (CVD). However, there are still gaps regarding large population risk assessment. Results from the nationwide Behavioral Risk Factor Surveillance System (BRFSS) were used along with air quality monitoring measurements to implement a systematic evaluation of PM-related CVD risks at the national and regional scales. CVD status and individual-level risk factors were collected from more than 500,000 BRFSS respondents across 2,231 contiguous U.S. counties for 2007 and 2009. Chronic exposures to PM pollutants were estimated with spatial modeling from measurement data. CVD outcomes attributable to PM pollutants were assessed by mixed-effects logistic regression and latent class regression (LCR), with adjustment for multicausality. There were positive associations between CVD and PM after accounting for competing risk factors: the multivariable-adjusted odds for the multiplicity of CVD outcomes increased by 1.32 (95% confidence interval: 1.23–1.43) and 1.15 (1.07–1.22) times per 10 µg/m3 increase in PM2.5 and PM10 respectively in the LCR analyses. After controlling for spatial confounding, there were moderate estimated effects of PM exposure on multiple cardiovascular manifestations. These results suggest that chronic exposures to ambient particulates are important environmental risk factors for cardiovascular morbidity

Communicating with parents of obese children: Which channels are most effective?

One of the strategies proven most successful in curbing rising rates of childhood obesity involves targeting parents as agents of change. Prior studies have focused on what messages to communicate, but few have investigated how they should be communicated.To identify the channels most effective for communicating with parents of overweight and obese children and understand whether their use of parenting information sources differs from others in the community.This study utilizes data from the Longitudinal Study of Australian Children (LSAC). Families were included if weight and height information was available for parents and children at three data collection points: Waves 1, 2 and 4 (collected 2004, 2006 and 2010, respectively, n = 5107).A priori and a posteriori segmentation methods identified groups of parents that were similar in the sources used to obtain information about parenting, and examined whether some segments were more likely to have obese children.Four segments were identified that differed in their information source use: the 'personal networks', 'books', 'official sources' and 'mixed approach' segments. The 'official sources' and 'mixed approach' segments were most likely to have obese children, and they used doctors, government/community organizations and friends to obtain information on parenting. These segments were also less educated and had lower employment.Messages are most likely to reach families with obese children if communicated through doctors, government publications and community organizations. Further, messages targeting social groupings of parents will leverage the power of advice from friends, which is another valuable information source for this group