Conditional standard deviation

Analyse the same sample several times under r, R, or R conditions Standard Deviation... 

Estimating o flows from the mean reversion estimation process. It estimates the conditional standard deviation of short-term interest rates using the GARCH(1, 1) model ... 

Figure 15. -Galactosidase Assay DDMC3(samplel lO.Omg/ml, sample2 20.0mg/ml, samples 28.6mg/ml), weight increase 130% DEAE-dextran(10mg/ml), weight increase 0%. Each condition represents the mean of three transfecrions per condition. Standard deviation was calculated and plotted for each condition.

Lin et al. (2013 a) for the first time used the term conditional spectrum which was used to represent an analytical distribution of response spectra in the manner described here. The CS builds upon the CMS (which focuses on the mean) and includes a measure of the variance in addition to the mean. Figure la depicts the analytical distribution of the conditional spectrum with conditional mean spectrum as the thick solid line as well as conditional mean +/— conditional standard deviation as the thick dashed lines. Lin et al. (2013b, c) utilized the conditional spectrum to select ground motions for nonlinear dynamic analysis (also known as response history... 

The conditional standard deviation < i iSa(Ti) i ,Sa(T y whcn combined with the... 

Conditional Spectra, Fig. 3 (a) Conditional means and (b) conditional standard deviations of the CS computed using... 

Fig. 7 Respraise spectrum conditioned on S (To) = 0.22 gat To = 2.5 s. (a) Exponential of the eraiditional mean of InSafT. (b) Conditional standard deviation of...

The solvent effects are generally less than 1 ppm, which are well within the error bounds of the standard deviations of the calculated shifts. It is possible, however, that under extreme conditions larger deviations may be observed. 

Precision is a measure of the spread of data about a central value and may be expressed as the range, the standard deviation, or the variance. Precision is commonly divided into two categories repeatability and reproducibility. Repeatability is the precision obtained when all measurements are made by the same analyst during a single period of laboratory work, using the same solutions and equipment. Reproducibility, on the other hand, is the precision obtained under any other set of conditions, including that between analysts, or between laboratory sessions for a single analyst. Since reproducibility includes additional sources of variability, the reproducibility of an analysis can be no better than its repeatability. 

Few populations, however, meet the conditions for a true binomial distribution. Real populations normally contain more than two types of particles, with the analyte present at several levels of concentration. Nevertheless, many well-mixed populations, in which the population s composition is homogeneous on the scale at which we sample, approximate binomial sampling statistics. Under these conditions the following relationship between the mass of a randomly collected grab sample, m, and the percent relative standard deviation for sampling, R, is often valid. ... 

Sutton Micrometeorology, McGraw-Hill, 1953, p, 286) developed a solution to the above difficulty by defining dispersion coefficients, O, Gy, and O, defined as the standard deviation of the concentrations in the downwind, crosswind, and vertical x, y, z) directions, respectively, The dispersion coefficients are a function of atmospheric conditions and the distance downwind from the release. The atmospheric conditions are classified into six stability classes (A through F) for continuous releases and three stability classes (unstable, neutral, and stable) for instantaneous releases. The stability classes depend on wind speed and the amount of sunlight, as shown in Table 26-28,... 

Investigated is the influence of the purity degree and concentration of sulfuric acid used for samples dissolution, on the analysis precision. Chosen are optimum conditions of sample preparation for the analysis excluding loss of Ce(IV) due to its interaction with organic impurities-reducers present in sulfuric acid. The photometric technique for Ce(IV) 0.002 - 0.1 % determination in alkaline and rare-earth borates is worked out. The technique based on o-tolidine oxidation by Ce(IV). The relative standard deviation is 0.02-0.1. 

As the result of the performed investigations was offered to make direct photometric determination of Nd microgram quantities in the presence of 500-fold and 1100-fold quantities of Mo and Pb correspondingly. The rare earth determination procedure involves sample dissolution in HCI, molybdenum reduction to Mo (V) by hydrazine and lead and Mo (V) masking by EDTA. The maximal colour development of Nd-arsenazo III complex was obtained at pH 2,7-2,8. The optimal condition of Nd determination that was established permit to estimate Nd without separation in solution after sample decomposition. Relative standard deviations at determination of 5-20 p.g of Nd from 0,1 g PbMoO are 0,1-0,03. The received data allow to use the offered procedure for solving of wide circle of analytical problems. 

Figure 7 The production and emission of NO during denitrification in agricultural soil treated with NO3 fertilizer (KNO3) and the nitrification inhibitor Dyciandiamide (10%) under aerobic (air) and anerobic conditions (N,). Fluxes are means from three soil columns, error bars represent standard deviations from the mean. V = vertical flow through the column H = Horizontal flow over the soil surface.

Plotting this data as a Pareto chart gives Figure 3. It shows that the load is the dominant variable in the problem and so the stress is very sensitive to changes in the load, but the dimensional variables have little impact on the problem. Under conditions where the standard deviation of the dimensional variables increased for whatever reason, their impact on the stress distribution would increase to the detriment of the contribution made by the load if its standard deviation remained the same. 

It is known that the vertical distribution of diffusing particles from an elevated point source is a function of the standard deviation of the vertical wind direction at the release point. The standard deviations of the vertical and horizontal wind directions are related to the standard deviations of particle concentrations in the vertical and horizontal directions within the plume itself. This is equivalent to saying that fluctuations in stack top conditions control the distribution of pollutant in the plume. Furthermore, it is known that the plume pollutant distributions follow a familiar Gaussian diffusion equation. 

No calibration was required and the percentage of only one element needed to be established, for the alloy was binary. The atomic numbers of copper and zinc being adjacent, the intensity ratio of their K lines could, after an appropriate adjustment of experimental conditions, be assumed equal to the ratio of the number of atoms present of each metal. Under these simple conditions, compositions could be calculated satisfactorily from intensity ratios, as is shown by the following results for a series of 16 x-ray determinations on such an alloy found by chemical methods (details not given) to contain 73.00% copper average copper content, 73.16% standard deviation for a single determination, 0.27%... 

For the usual accurate analytical method, the mean f is assumed identical with the true value, and observed errors are attributed to an indefinitely large number of small causes operating at random. The standard deviation, s, depends upon these small causes and may assume any value mean and standard deviation are wholly independent, so that an infinite number of distribution curves is conceivable. As we have seen, x-ray emission spectrography considered as a random process differs sharply from such a usual case. Under ideal conditions, the individual counts must lie upon the unique Gaussian curve for which the standard deviation is the square root of the mean. This unique Gaussian is a fluctuation curve, not an error curve in the strictest sense there is no true value of N such as that presumably corresponding to a of Section 10.1—there is only a most probable value N. 

Inasmuch as sc results from fluctuations that cannot be eliminated so long as quanta are counted, this standard deviation is the irreducible minimum for x-ray emission spectrography under ideal conditions. Not only is it a minimum, but it is also a predictable minimum. When the standard deviation, s, significantly exceeds the standard counting error, sc, it is likely that errors resembling those the analytical chemist usually encounters are superimposed upon the random fluctuations associated with the emission process. 

Table I. Photosynthetic rates (mean standard deviation n=3) for samples taken from three different habitats and incubated for 4 hours under the four experimental conditions described in the text (Amb = ambient UV Exc =...

Table 12,2. Experimental conditions, mean 5 N values and diet-tissue and tissue-tissue dilTerence values (A N) of rats not subjected to water stress and/or heat stress, Diet 8 N values are those of the protein source rather than the whole diet pellets. SD = standard deviation, co-d = collagen-diet, h-d = hair-dici, f-d = flesh-diet, co-f = collagen-flesh. 

For the speed and load distributions three superposed normal distributions around three fixed mean values are used, corresponding for the speed to town, country road, and motorway (turnpike or freeway) traffic. A maximum speed fixes the total width of the curve from zero to that maximum. This corresponds to lOtr, where a stands for standard deviation of the three superposed distributions. The three mean values are fixed at 3, 5, and la. Their heights can be varied according to the frequency with which the three distributions occur, their sum has to add up to LA similar distribution is also used to describe the different load conditions with low, medium, and high loads. Figure 26.79 gives an example of such a triple distribution function. 

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