Deviation, geometric standard

The median and geometric standard deviation for the distribution of CDio values in each chemical-species combination were obtained by using a mixed-effects model of the form 

The maximum likelihood estimate for a, the ln(GSD), was also obtained, and is used in some of the figures in the text However, the profile Ukefihood for the a is not well-approximated by a Gaussian form, so in further analysis the full profile likelihood was used. 

The loglikelihoods used in Section 27.8.2 were summed across aU chemical—species combinations and used to test hypotheses about 7 using Ukefihood ratio tests. Care was taken to select only those chemical-species combinations that contributed information to the test for example, those chemical-species combinations with only one measurement have to be excluded (since they contain no information on the a). There are 772 chemical-species combinations with more than one measurement, 3 

Kilion, B., Hogg, M. L., Tudor, J., and Keller, B. (1987). Investigation of cancer risk assessment methods (4 parts Summary and Vols. 1-3) EPA/600/6-87/007a,b,c,d. 

and Shipp, A. M. (1988). Correlation between carcinogenic potency of chemicals in animals and humans. Risk Anal 8(4), 531-544. 

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The size of inhaled particles varies markedly. The size distribution approximates a log-normal distribution that can be described by the median or the geometric mean, and by the geometric standard deviation. For fibers, both... 

Aerosol, monodisperse An aerosol with a size-distribution function described by a geometrical standard deviation less than 1.15. If the deviation is between 1.15 and 1.5, it is classified as a quasi-mono-disperse aerosol. 

Geometrical standard deviation A measure of the range of particulate sizes present in a collection of particles. 

Irani and Callis (Ref 14) used two parameters of the distribution of ground monocalcium phosphate (which follows the commonly used log normal distribution law) namely, Mg and Og, the geometric mean diameter and the geometric standard deviation, to evaluate the precision and accuracy of electro-formed sieves vs sedimentation as a reference procedure ... 

The foregoing close agreement of the geometric mean diameter and geometric standard deviation results indicates that accuracy evaluations were made on an absolute scale, and did not refer to some arbitrary scale... 

AMAD = activity median aerodynamic GSD = geometric standard deviation... 

Data on surface radium concentrations has been compiled for 394 of the 474 quadrangles covering the conterminous 48 states. The resulting distribution is illustrated in Figure 2, where the parameters shown for the distribution are calculated from the binned data. This distribution has a GM of 25 Bq kg and geometric standard deviation (GSD) of 1.75. Based on this distribution, approximately 20% of the surface radium concentration data are above 40 Bq kg and 0.7% are above 100 Bq kg... 

The only information presently available on the national frequency distribution of indoor radon levels is a 1984 analysis by Nero at the Lawrence Berkley Laboratory (Nero et al., 1984). Using data from about 500 houses, Nero developed a frequency distribution of radon levels in U.S. single family houses. This distribution is characterized by a geometric mean of 0.9 pCi/L and a geometric standard deviation of 2.8. 

Theoretical calculations of unattached fractions of radon progeny require prediction of an attachment coefficient. Average attachment coefficients for aerosols of various count median diameters, CMD, and geometric standard deviations, ag, are calculated using four different theories. These theories are ... 

Theoretical calculations of unattached fractions of radon or thoron progeny involve four important parameters, namely, 1) the count median diameter of the aerosol, 2) the geometric standard deviation of the particle size distribution, 3) the aerosol concentration, and 4) the age of the air. All of these parameters have a significant effect on the theoretical calculation of the unattached fraction and should be reported with theoretical or experimental values of the unattached fraction. 

Figures 3 and 4 show the variation of the attachment coefficient with count median diameter for the diffusion, kinetic, hybrid and kinetic-diffusion theory for geometric standard deviations of 2 and 3 respectively.

Figure 5 illustrates the effect of the geometric standard deviation on the attachment coefficient using the hybrid theory. 

In Figs. 6 and 7 the attachment coefficient is plotted against the geometric standard deviation using the four theories, for count median diameters of 0.2 ym and 0.3 ym respectively. 

An aerosol size distribution can, therefore, be described in terms of the count median diameter, d, and the geometric standard deviation, a These parameters were obtained from experimental data using a diffusion battery method (Busigin et al., 1980). A diffusion battery is an assembly of a number of cylindrical or rectangular channels. The relative penetration of aerosols through different sizes of diffusion batteries at specified flow rates allows the aerosol size distribution to be calculated. 

Table IV. Activity and Aerosol Size Distributions, Count Median Diameter (CMD) and the Geometric Standard Deviation (indicated in brackets)...

Table II. Summary of Mean Monthly Activity Median Aerodynamic Diameters (AMAD) and Geometric Standard Deviations (tfg) of Radon and Thoron Daughter Size Distributions in Ambient Aerosols...

Table III. Median Aerodynamic Diameters (MAD) and Geometric Standard Deviations (Og) of Pb-210 and Be-7 Based on Radioactivity and SO Measured with High-Volume Cascade Impactors...

Fig. 1. Deposition of inhaled particles of different sizes (mass median aerodynamic diameters) in the three regions of the respiratory tract. Each shaded area indicates the variability of deposition when the aerosol distribution parameter, o, (geometric standard deviation) was varied from 1.2 to 4.5. The assumed tidal volume was 1450 cm3. (Reproduced from Health Physics, vol. 12, pp. 173-207,1966 by permission of the Health Physics Society).

Activity median aerodynamic diameter h Geometric standard deviation. 

Boecker, 1973) exposed to other radioactive aerosols was also reviewed. An analysis of the data from both studies suggested that for beagles exposed by inhalation to radioactive 144Ce aerosols, individuals in the population would receive radiation doses to a given organ within a fog-normal distribution characterized by a geometric standard deviation of 2. 

Concentratons of Sr in people living in New York City between 1953 and 1959 who were exposed to nuclear weapons fallout were reported by Kulp and Schulert (1962). They suggested that the distribution of observed values was well fit by a log-normal distribution that had a geometric standard deviation of about 1.7. The Federal Radiation Council (FRC, 1961), after review of the accumulated data on Sr in human bone, concluded that a log-normal distribution was the appropriate description of the distribution of this age-controlled, exposuretime controlled population. The main exposure to Sr from fallout was by way of ingestion. 

The droplet size distribution produced by vaporization-condensation technique is strongly dependent on the chemical composition and properties of the liquid. If well controlled on a small scale, vaporization-condensation technique can produce moderately mono-disperse sprays with geometric standard deviations ranging from about 1.2 to 1.8.[88]... 

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