Some case studies of skewed (and other ab-normal) data distributions arising in low-level environmental research

Three general classes of skewed data distributions have been encountered in research on background radiation, chemical and radiochemical blanks, and low levels of Kr-85 and C-14 in the atmosphere and the cryosphere. The first class of skewed data can be considered to be theoretically, or fundamentally skewed. It is typified by the exponential distribution of inter-arrival times for nuclear counting events for a Poisson process. As part of a study of the nature of low-level (anti-coincidence) Geiger-Muller counter background radiation, tests were performed on the Poisson distribution of counts, the uniform distribution of arrival times, and the exponential distribution of inter-arrival times. The real laboratory system, of course, failed the (inter-arrival time) test - for very interesting reasons, linked to the physics of the measurement process. The second, computationally skewed, class relates to skewness induced by non-linear transformations. It is illustrated by non-linear concentration estimates from inverse calibration, and bivariate blank corrections for low-level C-14-C-12 aerosol data that led to highly asymmetric uncertainty intervals for the biomass carbon contribution to urban "soot". The third, environmentally skewed, data class relates to a universal problem for the detection of excursions above blank or baseline levels: namely, the widespread occurrence of ab-normal distributions of environmental and laboratory blanks. This is illustrated by the search for fundamental factors that lurk behind skewed frequency distributions of sulfur laboratory blanks and Kr-85 environmental baselines, and the application of robust statistical procedures for reliable detection decisions in the face of skewed isotopic carbon procedural blanks with few degrees of freedom.