Gaussian distribution mean width

Figure 4.51. Distribution of experimental data. Six experimental formulations (strengths 1, 2, resp. 3 for formulations A, respectively B) were tested for cumulative release at five sampling times (10, 20, 30, 45, respectively 60 min.). Twelve tablets of each formulation were tested, for a total of 347 measurements (13 data points were lost to equipment malfunction and handling errors). The group means were normalized to 100% and the distribution of all points was calculated (bin width 0.5%, her depicted as a trace). The central portion is well represented by a combination of two Gaussian distributions centered on = 100, one that represents the majority of points, see Fig. 4.52, and another that is essentially due to the 10-minute data for formulation B. The data point marked with an arrow and the asymmetry must be ignored if a reasonable model is to be fit. There is room for some variation of the coefficients, as is demonstrated by the two representative curves (gray coefficients in parentheses, h = peak height, s = SD), that all yield very similar GOF-figures. (See Table 3.4.)...

Figure 21.2—Gaussian distribution. As the number of measurements increases and the width of the interval remains relatively narrow, the envelope of data points (frequency vs measurements) resembles that of a Gaussian curve (normal distribution). The bottom figure represents two series of results with two different means. If the number of measurements is very small, it is not possible to estimate the average distribution. At the bottom right, the reduced form of the Gaussian distribution is shown.

Gaussian distribution Theoretical bell-shaped distribution of measurements when all error is random. The center of the curve is the mean, p, and the width is characterized by the standard deviation, a. A nortnalized Gaussian distribution, also called the normal error curve, has an area of unity and is given by... 

Three commercial activated carbons were used BPL, CAL and GAe, manufactured by Chemviron, Calgon and CECA respectively. In addition, sample GAe-oxl was prepared by oxidation of GAe in aqueous solution of (NH4)2S20g and further pyrolysis in N2 flow at 773 K [5]. The specific surface areas were obtained applying the BET and Dubinin-Asthakov equations to the adsorption of N2 at 77 K and CO2 at 273 K respectively. Moreover, the C02 adsorption data permitted the evaluation of the micropore size distributions and the mean value of pore width using the Dubinin-Stoeckli equation [6] which supposes a gaussian distribution of pore sizes. 

Figure 3 Comparison of PSDs obtained using the Dubinin-Stoeckli (DS), Horvalh-Kawazoe (HK), and density fitnctional theory (DFT) methods to interpret an isotherm generated from molecular simulation of nitrogen adsorption in a model carbon that has an Gaussian distribution of slit pore widths (18]. Results are shown for mean pore widths of 8.9 A (left) and 16.9 A (right).

The small random crystal strains can be quantified and this is also given in Table 5. It was found that the sttain can be described by a Gaussian distribution characterised by a mean value, 8, of zero and a half width of 8a = 2cm . The analysis also differed from that of previous workers in both the hyperfine values and the requirement of a nuclear quadrupole term. The transitions within the lowest excited singlet could also be observed directly [31]. It can be concluded that the Cu(ll)/MgO system can be described as an almost pure dynamic Jahn-Teller case. 

In Eq. (13), Wi and W2 are measured at the base of each peak. For Gaussian peak distributions, these widths equal 4a, and a column resolution of 1.0 means that there is 4.6% overlap of peak 1 in peak 2 and vice versa a resolution of 1.5 means there is 0.3% overlap between the two peaks. Generally, the resolution for a given separation can be increased by lengthening the column and, thus, increasing the number of theoretical plates. Here again, the trade-off for this increased resolution is a longer retention time. 

Figure 11 shows the mean energy of 9-mer aggregates (bars) selected from a Gaussian distribution of otherwise identical monomer energies with width A. Clearly the distribution of 9-mer energies can be characterized by a width S and the relation holds, where a is the width of the energy distribution... 

This is the familiar bell-shaped error curve having a maximum at the mean value, y, and a width described by the standard distribution, a. The integral of the gaussian distribution over all values of the argument is unity. Because the function is symmetrical, the integral from the mean value over all values on either side is 0.5. 

GAUSsian distributions with 1/e values of about 8, 18, and 18 Mev respectively for Li, C, and 0. Due to approximations in the theory, the relative differences are more significant than the absolute values. Barton and Smith have compared the widths from He and Li, and find that the mean momentum of nucleons in He is higher than that in Li. It thus seems definite that the average momentum of the nucleons in Li is less than that of other light nuclei measured to date. 

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