Normalized Gaussian distribution

It is important to verify that the simulation describes the chemical system correctly. Any given property of the system should show a normal (Gaussian) distribution around the average value. If a normal distribution is not obtained, then a systematic error in the calculation is indicated. Comparing computed values to the experimental results will indicate the reasonableness of the force field, number of solvent molecules, and other aspects of the model system. [Pg.62]

The particle size distribution of ball-milled metals and minerals, and atomized metals, follows approximately the Gaussian or normal distribution, in most cases when the logarithn of die diameter is used rather dran the simple diameter. The normal Gaussian distribution equation is... [Pg.202]

The reason for calling equation 8.3-1 a "Gaussian diffusion model" is because it has the form of the normal/Gaussian distribution (equation 2.5-2). Concentration averages for long time intervals may be calculated by averaging the concentrations at grid elements over which the plume passes. [Pg.323]

The normal (Gaussian) distribution is the most frequently used probability function and is given by... [Pg.95]

If we consider an absorption band showing a normal (Gaussian) distribution [Fig. 17.13(a)], we find [Figs. (b) and (d)] that the first- and third-derivative plots are disperse functions that are unlike the original curve, but they can be used to fix accurately the wavelength of maximum absorption, Amax (point M in the diagram). [Pg.668]

Consider the log normal (Gaussian) distribution, of which an example is given as follows ... [Pg.220]

A further consideration is that the value of the calculated nonlinearity will depend not only on the function that fits the data, we suspect that it will also depend on the distribution of the data along the X-axis. Therefore, for pedagogical purposes, here we will consider the situation for two common data distributions the uniform distribution and the Normal (Gaussian) distribution. [Pg.453]

As was shown, the conventional method for data reconciliation is that of weighted least squares, in which the adjustments to the data are weighted by the inverse of the measurement noise covariance matrix so that the model constraints are satisfied. The main assumption of the conventional approach is that the errors follow a normal Gaussian distribution. When this assumption is satisfied, conventional approaches provide unbiased estimates of the plant states. The presence of gross errors violates the assumptions in the conventional approach and makes the results invalid. [Pg.218]

The formation of a boundary between the dextran solution and the dextran solution containing PVP 360 (concentration 5 kg m 3) yields an apparently normal Gaussian distribution of the material detected by Schlieren optics. The various apparent diffusion coefficients obtained by an analysis of the Schlieren curves, which include diffusion coefficients obtained by the reduced height-area ratio method, the reduced second-moment and the width-at-half-height method, show the same qualitative behavior although quantitative differences do exist. This is seen in Fig. 7 where the... [Pg.126]

The skewness k characterizes the asymmetry of the spectrum, whereas the excess k2 describes deviation of the levels or line density from the normal (Gaussian) distribution density. [Pg.381]

The exact formulation of the inlet and outlet boundary conditions becomes important only if the dispersion number (DjuL) is large (> 0.01). Fortunately, when DjuL is small (< 0.01) and the C-curve approximates to a normal Gaussian distribution, differences in behaviour between open and closed types of boundary condition are not significant. Also, for small dispersion numbers DjuL it has been shown rather surprisingly that we do not need to have ideal pulse injection in order to obtain dispersion coefficients from C-curves. A tracer pulse of any arbitrary shape is introduced at any convenient point upstream and the concentration measured over a period of time at both inlet and outlet of a reaction vessel whose dispersion characteristics are to be determined, as in Fig. 2.18. The means 7in and fout and the variances and out for each of the C-curves are found. [Pg.94]

The normal Gaussian distribution df coarse HMX impact sensy is used to estimate the increased sensy of coarse HMX contg various amounts of fine ( <63 microns) airborne grit by a statistical modeled expt. The exptl results were then used in a BemoulUan confidence level eqtn to determine the sample size required to accurately estimate the sensy of any grit contg HMX sample with a K % level of confidence. A sample of the type of K table derived is shown for HMX in Table 5]... [Pg.585]

Figure 8.1 Histogram showing a distribution of observed values, along with a Normal (Gaussian) distribution function.

Errors associated withy at each point xt should fit a normal (GAUSSian) distribution and should be free from outliers. The latter property can be tested by the DIXON... [Pg.51]

Figure 1 Normal (Gaussian) distribution, confidence limits, and confidence intervals.

With the availability of some 50 sets of handblanks (environmental-natural levels of Ba and Sb on hands), firing tests and calibrations, we considered a different concept for the interpretation of the results. The evaluation consisted of two steps 1) establishing that the Ba and Sb values of handblanks of the accumulated population sample followed a normal (Gaussian) distribution as statistically approximated by the t-Distribution, and 2) utilization of relatively simple statistical formalism for the calculation of the probability that the amount of Ba and Sb found on a given swab belongs to the established handblank population. (An appendix at the end of the paper may be useful to readers not normally utilizing statistics). [Pg.89]

It should be emphasized that for the Markovian copolymers, the knowledge of these structure parameters will suffice for finding the probabilities of any sequences LZ, i.e., for a comprehensive description of the structure of the chains of such copolymers at their given average composition. As for the CD of the Markovian copolymers, for any fraction of Z-mers it is described at Z 1 by the normal Gaussian distribution with covariance matrix, which is controlled along with Z only by the values of structure parameters (Lowry, 1970). The calculation of their dependence on time and on the kinetic parameters of a reaction system enables a complete statistical description of the chemical structure of a Markovian copolymer. It is obvious therewith to which extent a mathematical modeling of the processes of the synthesis of linear copolymers becomes simpler when the sequence of units in their macromolecules is known to obey Markov statistics. [Pg.172]

For many cases, especially if the spreading is small, the spreading function can be approximated by the normal Gaussian distribution function G in the form ... [Pg.167]

There is considerable individual variation in nutrient requirements. It is generally assumed that requirements follow a more or less statistically normal (Gaussian) distribution, as shown in the upper curve in Figure 1.1. This means that 95% of the population has a requirement for a given nutrient within the range of 2 SD about the observed mean requirement. Therefore, an intake at the level of the observed (or estimated) mean requirement plus 2 x SD will be more than enough to meet the requirements of 97.5% of the population. This is the level that is generally called the RDI, RDA, RNI, or PRI. [Pg.20]

Figure 5 Normal (Gaussian) distribution for (a) individual measurements,...

Figures Normal (Gaussian) distribution for (a) individual measurements, and (h) means of samples of measurements, with the areas enclosing 95% ( + 2 s) and 99.7% ( + 3 s) of the values shown in each rase...

In many instances, the normal (Gaussian) distribution best describes the observed pattern, giving a symmetrical, bell-shaped frequency distribution (p. 274) for example replicate measurements of a particular characteristic (e.g. rejjeated measurements of the end-point in a titration). [Pg.264]

Fig. I a, b. Plots for the determination of uniformity coefficients (reliability function) of phenolic foam samples during tensile tests (a) normal (Gaussian) distribution (b) Weibull s distribution )...

If, instead of one of the simple functions given in the Table, which are equal to zero for all r > B, a normalized Gaussian distribution is taken, that is, f(r) = fc exp (—fc, the Bertaut equation must be corrected... [Pg.165]

Figure 5.3.6. The Log (constant + normal Gaussian) distribution of masses for a large number of spectra.

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