Estimating the mean and standard deviation of concentration distributions using censored samples

Environmental data sets of pollutant concentrations in air, water, and soil frequently include unquantified sample values reported only as being below the analytical method detection limit. These values, referred to as censored values, should be considered in the estimation of distribution parameters as each represents some value of pollutant concentration between zero and the detection limit. Most of the currently accepted methods for estimating the population parameters of environmental data sets containing censored values rely upon the assumption of an underlying normal (or transformed normal) distribution. This assumption can result in unacceptable levels of error in parameter estimation due to the unbounded left tail of the normal distribution. With the beta distribution, which is bounded by the same range of a distribution of concentrations, $\rm\lbrack0\le x\le1\rbrack,$ parameter estimation errors resulting from improper distribution bounds are avoided. This work developed a method that uses the beta distribution to estimate population parameters from censored environmental data sets and evaluated its performance in comparison to currently accepted methods that rely upon an underlying normal (or transformed normal) distribution. Data sets were generated assuming typical values encountered in environmental pollutant evaluation for mean, standard deviation, and number of variates. For each set of model values, data sets were generated assuming that the data was distributed either normally, lognormally, or according to a beta distribution. For varying levels of censoring, two established methods of parameter estimation, regression on normal ordered statistics, and regression on lognormal ordered statistics, were used to estimate the known mean and standard deviation of each data set. The method developed for this study, employing a beta distribution assumption, was also used to estimate parameters and the relative accuracy of all three methods were compared. For data sets of all three distribution types, and for censoring levels up to 50%, the performance of the new method equaled, if not exceeded, the performance of the two established methods. Because of its robustness in parameter estimation regardless of distribution type or censoring level, the method employing the beta distribution should be considered for full development in estimating parameters for censored environmental data sets. ^

Qualitative behaviour of L1 and L2 standard deviation in insulations measurements according to standard UNE EN ISO 140-4

Knowledge of the uncertainty of measurement of testing results is important when results have to be compared with limits and specifications. In the measurement of sound insulation following standards UNE EN ISO 140-4 the uncertainty of the final magnitude is mainly associated to the average sound pressure levels L1 and L2 measured. A parameter that allows us to quantify the spatial variation of the sound pressure level is the standard deviation of the pressure levels measured at different points of the room. In this work, for a wide number of measurements following standards UNE EN ISO 140-4 we analyzed qualitatively the behaviour of the standard deviation for L1 and L2. The study of sound fields in enclosed spaces is very difficult. There are a wide variety of rooms with different sound fields depending on factors as volume, geometry and materials. In general, we observe that the L1 and L2 standard deviations contain peaks and dips independent on characteristics of the rooms at single frequencies that could correspond to critical frequencies of walls, floors and windows or even to temporal alterations of the sound field. Also, in most measurements according to UNE EN ISO 140-4 a large similitude between L1 and L2 standard deviation is found. We believe that such result points to a coupled system between source and receiving rooms, mainly at low frequencies the shape of the L1 and L2 standard deviations is comparable to the velocity level standard deviation on a wall

Tables describing small-sample properties of the mean, median, standard deviation, and other statistics in sampling from various distributions /

Mode of access: Internet.

Nitrogen fixation and nitrogen gene abundance of METEOR cruises M77/3 and M77/4

Nitrogen fixation, the biological reduction of dinitrogen gas (N2) to ammonium (NH4+), is quantitatively the most important external source of new nitrogen (N) to the open ocean. Classically, the ecological niche of oceanic N2 fixers (diazotrophs) is ascribed to tropical oligotrophic surface waters, often depleted in fixed N, with a diazotrophic community dominated by cyanobacteria. Although this applies for large areas of the ocean, biogeochemical models and phylogenetic studies suggest that the oceanic diazotrophic niche may be much broader than previously considered, resulting in major implications for the global N-budget. Here, we report on the composition, distribution and abundance of nifH, the functional gene marker for N2 fixation. Our results show the presence of eight clades of diazotrophs in the oxygen minimum zone (OMZ) off Peru. Although proteobacterial clades dominated overall, two clusters affiliated to spirochaeta and archaea were identified. N2 fixation was detected within OMZ waters and was stimulated by the addition of organic carbon sources supporting the view that non-phototrophic diazotrophs were actively fixing dinitrogen. The observed co-occurrence of key functional genes for N2 fixation, nitrification, anammox and denitrification suggests that a close spatial coupling of N-input and N-loss processes exists in the OMZ off Peru. The wide distribution of diazotrophs throughout the water column adds to the emerging view that the habitat of marine diazotrophs can be extended to low oxygen/high nitrate areas. Furthermore, our statistical analysis suggests that NO2- and PO43- are the major factors affecting diazotrophic distribution throughout the OMZ. In view of the predicted increase in ocean deoxygenation resulting from global warming, our findings indicate that the importance of OMZs as niches for N2 fixation may increase in the futur