Cumulative frequency distributions

Fig. 3. Cumulative frequency distribution plotted by A, number B, surface area and C, volume, for the data in Table 1.

If necessary, the fit can be improved by increasing the order of the polynomial part of Eq. (9-89), so that this approach provides a veiy flexible method of simulation of a cumulative-frequency distribution. The method can even be extended to J-shaped cui ves, which are characterized by a maximum frequency at x = 0 and decreasing frequency for increasing values of x, by considering the reflexion of the cui ve in the y axis to exist. The resulting single maximum cui ve can then be sampled correctly by Monte Carlo methods if the vertical scale is halved and only absolute values of x are considered. 

Figure 4.10 Cumulative frequency distribution for SAE 1018 yield strength data...

The use of various statistical techniques has been discussed (46) for two situations. For standard air quality networks with an extensive period of record, analysis of residuals, visual inspection of scatter diagrams, and comparison of cumulative frequency distributions are quite useful techniques for assessing model performance. For tracer studies the spatial coverage is better, so that identification of meiximum measured concentrations during each test is more feasible. However, temporal coverage is more limited with a specific number of tests not continuous in time. 

Figure 7 provides a cumulative frequency distribution of the maximum 8-hour standard In 15 cities In 1980-84. Shown on the graph Is the 10 mg/m3 WHO guideline value. It can be seen that the average maximum 8-hour level Is exceeded In about 50% of the cities. 

Cumulative Frequency Distribution of 3 D-optimal sampling times... 

Figure 3.7 Frequency and cumulative frequency distributions of 3D-optimal sampling times for the Gompertz model, given the observations for subject 4. Vertical lines split the cumulative empirical distribution into equal probability regions.

Frequency domain performance, involving comparison of cumulative frequency distributions of the observed data and model predictions. In many situations, considering the various sources of error discussed earlier, it may... 

The ACAT model is loosely based on the work of Amidon and Yu who found that seven equal transit time compartments are required to represent the observed cumulative frequency distribution for small intestine transit times [4], Their original compartmental absorption and transit (CAT) model was able to explain the oral plasma concentration profiles of atenolol [21]. 

Fig.l. Cumulative frequency distribution of all measurements during the heating season. 

Fig.2. Cumulative frequency distribution of measurements in 47 houses during sunnier and winter.

Figure 4. Cumulative frequency distributions of radon concentration for dwellings with different house constructions traditional wooden, ferro-concrete and prefabricated. Numbers, arithmetic means and S.D.s, geometric means, medians, and ranges of radon measurements are also indicated at the bottom of the figure.

The results from the first study suggest rather clearly that conversation group sizes are limited at about four individuals (one speaker and three listeners) (Dunbar et al. 1995). Fig. 3 plots the cumulative frequency distributions for the number of individuals that a speaker can reach (i.e. conversation group size less one, since there is always only one speaker at any given moment per conversation Dunbar et al. 1995). All three datasets in the sample suggest that the number of listeners rapidly approaches an asymptotic value at around three. 

Graphic representation of cumulative frequency distribution of selected effects as a function of concentration is also prepared where ratio of median effective concentration is considered for drug selectivity using different endpoints. 

TABLE 4-2 Cumulative Frequency Distribution of Hourly Average Oxidant Concentrations in Selected Cities. 1964-1965 ... 

Quantal dose-effect plots. Shaded boxes (and the accompanying bell-shaped curves) indicate the frequency distribution of doses of drug required to produce a specified effect that is, the percentage of animals that required a particular dose to exhibit the effect. The open boxes (and the corresponding colored curves) indicate the cumulative frequency distribution of responses, which are lognormally distributed. 

The two-dimensional Weibull distribution (Weibull, 1951) is often used to describe the cumulative frequency distribution of wind speeds (see Livingstone and Imboden (1993) for a review) ... 

Fig. 2. Error bounds for the cumulative frequency distribution of the spectral density for the velocity autocorrelation function using jU.0, /n2, and ja evaluated for a classical model of liquid argon.29...

FIGURE 5-4 Cumulative frequency distribution of the urinary excretion of 1-hydroxypyrene in people living in two rural districts of Burundi (A), in Bujumbura ( ) and in a reference group at the University of Montreal ( ). Source Viau et al. 2000. Reprinted with permission copyright 2000, International Archives of Occupational and Environmental Health. 

In the Monte Carlo analysis samples are drawn at random from the residue distribution and then from the apple consumption distribution to provide the data points for the intake distribution. This sequence is repeated several thousand times until a smooth intake distribution curve is produced. The intake distribution shown in Fig. 2.5 represents 20,000 samples drawn from the pesticide residues and apple consumption distributions shown in Figs 2.3 and 2.4. The bars represent the relative frequency of each intake level and the line is the cumulative frequency distribution. The distribution is very skewed and it can be seen that the cumulative frequency is nearing 100% when only the mid-point of the distribution is being approached. This means that very high intakes are relatively rare occurrences. 

The total number of drops passed along the trajectory required to achieve a stabilized cumulative frequency distribution depends on the steepness of the trajectory with more drops required for size categories with large settling velocities because the path lengths are smaller. 

For the Student distribution, the values of cumulative frequency F(t, v) are also known and tabulated [72] (or present in computer packages). Figure 5.5.3 shows the dependence between the cumulative frequency distribution F(x) and x for a N(0,1) distribution (trace A) and the dependence between the cumulative frequency distribution F(x, 3) and x for a Student distribution (trace B). 

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