Frequency of occurrence

To predict the properties of a population on the basis of a sample, it is necessary to know something about the population s expected distribution around its central value. The distribution of a population can be represented by plotting the frequency of occurrence of individual values as a function of the values themselves. Such plots are called prohahility distrihutions. Unfortunately, we are rarely able to calculate the exact probability distribution for a chemical system. In fact, the probability distribution can take any shape, depending on the nature of the chemical system being investigated. Fortunately many chemical systems display one of several common probability distributions. Two of these distributions, the binomial distribution and the normal distribution, are discussed next. 

Plot showing frequency of occurrence for members of a population. 

The probability of finding an atom of in cholesterol follows a binomial distribution, where X is the sought for frequency of occurrence of atoms, N is the number of C atoms in a molecule of cholesterol, and p is the probability of finding an atom of... 

The most commonly encountered continuous distribution is the Gaussian, or normal distrihution, where the frequency of occurrence for a value, X, is given by... 

The data in Table 4.12 are best displayed as a histogram, in which the frequency of occurrence for equal intervals of data is plotted versus the midpoint of each interval. Table 4.13 and figure 4.8 show a frequency table and histogram for the data in Table 4.12. Note that the histogram was constructed such that the mean value for the data set is centered within its interval. In addition, a normal distribution curve using X and to estimate p, and is superimposed on the histogram. 

Based on the frequency of occurrence for each residue in the sequence of 207 unrelated proteins (8). 

The importance of determining a relationship between the magnitude of the exposure and the frequency of occurrence of a toxic effect is considered in detail below. 

Fig. 2. Histograms representing (a), the frequency of occurrence of platelets (PLT) and red blood cells (RBC) and illustrating coincidence where SL is low angle scatter, 2°C—3° and SH is high angle scatter, 5°C—15° (b), the volume of RBC, from 0 to 200 fL (c), the hemoglobin (HGB) concentration from 0 to...

Po adrninistered nifedipine is almost completely absorbed. The onset of action is 20 min and peak effects occur at 1—2 h. The principal route of elimination is through hepatic metaboHsm by oxidation to hydroxycarboxyHc acid and the corresponding lactone. These metaboHtes are pharmacologically inactive. Almost 70—80% of dmg is eliminated in the urine during the first 24 h. About 15% is excreted in the feces. The elimination half-life of nifedipine is about 1—2.5 h (1,98,99). Frequency of occurrence of side effects in patients is about 17% with about 5% requiring discontinuation of therapy (1,98,99). 

FIG. 8-38 Histogram plotting frequency of occurrence, c = mean, <3 = rms deviation. Also shown is fit by normal probability distribution. 

When X represents a continuous variable quantity, it is sometimes convenient to take the total or relative frequency of occurrences within a given range of x values. These frequencies can then be plotted against the midvalues of x to form a histogram. In this case, the ordinate should be the frequency per unit of width x. This makes the area under any bar proportional to the probability that the value of x will he in the given range. If the relative frequency is plotted as ordinate, the sum of the areas under the bars is unity. 

I. A CMR motor therefore can be operated at higher outputs on short-time duties as shown in curve (d). The extent to which a CMR motor cun be over-rated to perform a particular short-time or intermittent duty is considered in the follow ing example. While evaluating the rating for such duties, the heat during start-up and during braking and their frequency of occurrence should be considered. 

Note This operating condition is, however, not specific for it does not stipulate the frequency of occurrence of such a contingency. It may be assumed that this condition will not occur more than once before thermal stability is reached. See also Section 3.7. In normal practice a motor meeting the other operating conditions noted above in all likelihood will satisfy this requirement also without needing yet another derating. See also Example 7,1. 

This will also decrease in the same proportion as the increase in slip. For a rough estimate, we may also ignore the higher slip losses for an equal reduction in the required kW. However, due to the lower voltage the motor current will increase proportionately and will be /,/0.8 or 1.25/,. The motor will thus run overloaded by 25% for 20 minutes which is likely, and not more than once an hour. The frequency of occurrence must be known. A higher derating may be necessary if such a condition is frequent. 

A measure of the expected probability or frequency of occurrence of an event... 

Larsen (18-21) has developed averaging time models for use in analysis and interpretation of air quality data. For urban areas where concentrations for a given averaging time tend to be lognormally distributed, that is, where a plot of the log of concentration versus the cumulative frequency of occurrence on a normal frequency distribution scale is nearly linear,... 

Relative frequency of occurrence of D stability" Relative frequency of calms distributed above with D stability = 0.5753. 54,6058... 

The frequency of occurrence of winds from each of the 36 direchons for the two sites is given in the second and third columns of Table 21-6. Knoxville has its maximum from 240°, with frequent winds also from adjacent points. There is a secondary maximum across the compass (in the vicinity of 60°). Nashville, on the other hand, seems to have only one principal maximum (from 180°). To explore the magnitude of the differences, the fourth column is the difference for each direchon. Summing the absolute values of the differences and expressing them as a percentage of the total number of hours of observations shows that the differences constitute 62% of the total. 

Pits occur as small areas of localized corrosion and vary in size, frequency of occurrence, and depth. Rapid penetration of the metal may occur, leading to metal perforation. Pits are often initiated because of inhomogeneity of the metal surface, deposits on the surface, or breaks in a passive film. The intensity of attack is related to the ratio of cathode area to anode ai ea (pit site), as well as the effect of the environment. Halide ions such as chlorides often stimulate pitting corrosion. Once a pit starts, a concentration-cell is developed since the base of the pit is less accessible to oxygen. 

Total frequencies of environmental illness are difficult to measure. When causes can be identified, however, scientists observe that frequencies of occurrence of a particular illness vary directly with the severity and extent of exposure. Particularly frequent in the workplace are skin lesions from many different causes and pulmonary diseases related to the inhalation of various dusts, such as coal dust (black lung), cotton dust (brown lung), asbestos fibers (asbestosis), and silica dust (silicosis). Environmental agents can also cause biological effects without overt clinical illness (for example, chromosome damage from irradiation). 

Bimodal Distribution a plot of frequency of occurrence of a variable versus the variable. A bimodal distribution exists if there are two maxima of the frequency of occurrence separated by a minimum. See Mode. 

Mode the maximum point in a plot of the frequency of occurrence of a variable versus the variable. 

These and other incidents summarized in Table 5.3-1, are taken from the PSA Procedures lide (NUREG/CR-23(X3). The evidence of this experience is that flooding is a crec snt ible 5.3-2 (ibid.) presents the frequency of occurrence using the following categories ... 

Primary emphasis is often placed on the frequently occurring initiators, but they may not present the largest public health risk. To gain a perception of the relative importance of various initiators, Table 6.3-6 from Taylor et al, (1986) shows an ordering of the accident initiators for Indian Point 3 by Inspection Importance (Section 2.8.2) which considers both frequency of occurrence and health effects based on of one or more latent fatalities. 

Histogram A diagram of the frequency of occurrences of values of a variable, grouped according to value in a number of separate ranges. 

Overpressure can lead directly to all three hazards. It can lead directly and immediately to injury, to fire or explosion if there is an ignition source, and to pollution if there is not enough containment. Therefore, we must have a very high level of assurance that overpressure is going to have a very low frequency of occurrence. 

All sites have approximately same frequency of occurrence... 

WRPLOT is an interactive program tliat generates wind rose statistics and plots for selected meteorological stations for user-specified date and time ranges. A wind rose depicts die frequency of occurrence of winds in each of 16 direction sectors (north, nordi-northcast, nordieast, etc.) and six wind speed classes for a given location and time period. 

In a more quantitative sense, cause-consequence analysis may be viewed as a blend of fault tree end event tree analysis (discussed in tlie two preceding cliapters) for evaluating potential accidents. A major strengtli of cause-consequence analysis is its use as a communication tool. For example, a cause-consequence diagram displays the interrelationships between tlie accident outcomes (consequences) and Uieir basic causes. The method can be used to quantify the expected frequency of occurrence of the consequences if the appropriate chita are available. 

Tliis part of tlie book reviews and develops quantitative metliods for tlie analysis of liazard conditions in terms of the frequency of occurrence of unfavorable consequences. Uncertainty characterizes not only Uie transformation of a liazard into an accident, disaster, or catastrophe, but also tlie effects of such a transformation. Measurement of uncertainty falls witliin tlie purview of matliematical probability. Accordingly, Chapter 19 presents fundamental concepts and Uieorems of probability used in risk assessment. Chapter 20 discusses special probability distributions and teclmiques pertinent to risk assessment, and Chapter 21 presents actual case studies illustrating teclmiques in liazard risk assessment tliat use probability concepts, tlieorems, and special distributions. 

Frequency of Occurrence of Amino Acid Residues in Proteins... 

Frequency of occurrence of each amino acid re.sidue in the polypeptide chain.s of 207 unrelated protein.s of known. sequence. 

FIGURE 6.39 Relative frequencies of occurrence of amino acid residues in m-helices, /3-sheets, and /S-turns in proteins of known structure. (Adapted from Belt, J E., and Belt, E. T, 1988, Proteins and. Enzymes, Englewood Cliffs, NJ Prentice-Hall.)... 

Figure 6.S Frequency of occurrence of various stoichiometries among boride phases ...

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