Hypothetical distribution

Figure 8-62 depicts a hypothetical distributed control system. A number of different unit configurations are illustrated. This system consists of many commonly used DCS components, including multiplexers (MUXs), single/multiple-loop controllers, programmable logic controllers (PLCs), and smart devices. A typical system includes the following elements as well ... 

Section 1.6.2 discussed some theoretical distributions which are defined by more or less complicated mathematical formulae they aim at modeling real empirical data distributions or are used in statistical tests. There are some reasons to believe that phenomena observed in nature indeed follow such distributions. The normal distribution is the most widely used distribution in statistics, and it is fully determined by the mean value p. and the standard deviation a. For practical data these two parameters have to be estimated using the data at hand. This section discusses some possibilities to estimate the mean or central value, and the next section mentions different estimators for the standard deviation or spread the described criteria are fisted in Table 1.2. The choice of the estimator depends mainly on the data quality. Do the data really follow the underlying hypothetical distribution Or are there outliers or extreme values that could influence classical estimators and call for robust counterparts ... 

Figure 3.3 Hypothetical distribution of dipole moment magnitudes from a simulation of liquid water. The dashed curve is generated by connecting the tops of histogram bins whose height is dictated by the number of water molecules found to have dipole moments in the range spanned by the bin. Note that although the example is illustrated to be symmetric about a central value (which will thus necessarily be (/z)) this need not be the case...

The generation of photoexcited species at a particular position in the film structure has been shown in (6.19) and (6.20) to be proportional to the product of the modulus squared of the electric field, the refractive index, and the absorption coefficient. The optical electric field is strongly influenced by the mirror electrode. In order to illustrate the difference between single (ITO/polymer/Al) and bilayer (ITO/polymer/Ceo/Al) devices, hypothetical distributions of the optical field inside the device are indicated by the gray dashed line in Fig. 6.1. Simulation of a bilayer diode (Fig. 6.1b) clearly demonstrates that geometries may now be chosen to optimize the device, by moving the dissociation region from the node at the metal contact to the heterojunction. Since the exciton dissociation in bilayer devices occurs near the interface of the photoactive materials with distinct electroaffinity values, the boundary condition imposed by the mirror electrode can be used to maximize the optical electric field E 2 at this interface [17]. 

Figure 1.10 (A) Plot of NO versus PO) from all depths and from selected WOCE cruises in all ocean basins (A16,P16,I8NI9S). The inset shows how the various processes influence the NO versus PO) distribution. The solid line represents the mean ocean trend with a slope of 16 1, while the thinner lines show trends of constant N (see text for deflnition). (B) Hypothetical distribution of NOy versus PO) in a situation of excess NOy. (C) as (B), except for a situation of a NOy deficit. It is unclear why the intercept of the mean oceanic trendline in (A) is so close to zero. From Gruber (2004).

Figure 2.9 Cross-section showing hypothetical distribution of the three subsystems of burial-induced groundwater flow (geological cross-section of the Viking Graben, North Sea, adapted from Doligez et al., 1987. Reprinted by permission of Graham and Trotman Ltd.).

Figure 16=3 Observed and hypothetical distributions of 500 triglycerides values in serum (in mmol/L). A, The vertical bars of the left histogram show the number of observations in the Interval divided by the total number of observations. The curve is the estimated probability distribution of the population, assuming random sampling and a log-Gaussian distribution.

Fig. 14-5 Hypothetical distribution of P and temperature in a temperate lake in summer. Thermal stratification restricts exchange between surface and deep waters. Phosphorus is depleted in the surface waters by the sinking of biologically produced particles.

Figure 8-3 Hypothetical distribution of highest attained ranks and total numbers of filled positions on a scientific ladder...

Fig. 13. Hypothetical distribution of charges in a lamellar donor-acceptor system.

FIGURE 26.4 Hypothetical distributions of atmospheric concentrations (a) histogram and (b) continuous distribution. 

Figure 8.13 shows a hypothetical distribution when the recorded intensities of H, H,and are plotted against EdEldx. 

Hypothetical distribution density of ELISA results of populations of noninfected (left-hand curve) and infected (right-hand curve) individuals. The FN and FP area is referred to as "gray area," and results falling here must be regarded as suspect. The importance of retesting depends on how important the result is to classification of the test unit. The setting up of cutoff values depends on knowledge of such overlaps and the variability of the test used. 

The previous tests served the purpose of detecting differences between means or variances. The goodness of fit between an observed and a hypothetical distribution is done by two additional tests, the and the Kolmogorov-Smirnov tests. 

Test The goodness-of-fit test is used to test whether the observations of a population are sampled from a hypothetical distribution density function, for example, the normal distribution, at a given significance level a. The null and alternative hypotheses correspond to the following ... 

The spectrophotometric measurements in Table 2.1 are to be tested versus a normal distribution by means of Kolmogorov-Smirnov s test at a significance level of a = 0.05. In the first step, the empirical distribution function, F x), is evaluated as shown in Figure 2.10. For comparison of the hypothetical distribution function, the cumulative frequency by using the mean and the standard deviation of the data in dependence on the (standard normal) deviate z are plotted (cf. Eq. (2.28)). 

After evaluation of the hypothetical distribution function f(,(x), the difference between both distributions is computed. 

Figure 3.1 Hypothetical distribution of solutes NaCI and HOAc between ether and water-immiscible phases.

Figure 3 shows the map of the necropolis and the. network of individual displacements across tombs. This distribution was tested for discontinuities and was proved to be not statistically different from a hypothetical distribution of uniform utilization based on population densities at each tomb (Kolmogorov test, P < 0.05). The areas enclosed in the three polygons revealed a similar preferential utilization of the necropolis in the three seasons analysed. 

Figure 5.3 Hypothetical distribution of exchange time constants in a protein that is approximately 70% structured. The separation between the two modes allows for the comparison between the expected and actual amount of exchange In a given region of the protein, particularly at millisecond labeling times where the contribution from backbone amides involv in secondary structure is negligible...

Normal Distribution a hypothetical distribution that would be expected when completely random, continuous data is collected from a population. The normal distribution is commonly referred to as the bell-shaped curve because of its noted shape,... 

Fio. la. Hypothetical distribution curve for normal population (mean and standard... 

Fig. 16. Hypothetical distribution curve for positively skewed population (mean, median, and mode shown).

Figure 10.1 The hypothetical distribution of enantiomer fractions (EFs) for a chiral compound in different compartments of the ecosystem. The deviations from the racemic mixture are above and below the line EF = 0.5 [5].

Fig. 2.2 Hypothetical distribution of internal energies of ions formed in a typical beam-type instrument. Ions with dissociation rate constants <10 s" remain intact on the timescale of the mass spectrometer (10 s). Those with rate constants > 10 s" are unstable ions and fragment in the ion source, while the intermediate situation (10 10 s" ) represents metastable ions...

A. Two copper particles are placed in an aqueous environment and an electric field is applied. The polarization of each particle is shown. Initially the particle on the right liberates copper ions r le the particle on the left reduces water. The shaded area represents a hypothetical distribution of the ionic cloud. (For clarity only the phenomena in the inteiparticle region are shown). 

An example illustrating this approach is shown in the hypothetical distribution given below. 

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