Percentile

This expression is known as the vapor lock index (VLI) or the front-end volatility index (EEVI). The value of n for U.S. cars is generally reported as 9 when RVP is in kPa (0.13 when pressure is in psi) (23). The maximum level of VLI is set by month and by region according to the ninetieth percentile daily maximum temperature. 

Standard deviations from two to five or more. This means that the upper seventeenth percentile may be as much as from two to five times the mean. This variabihty is compounded by the problem of estimating the exposure of a group of workers having differing exposures to find the most exposed workers. Compared to this environmental variabihty, the variabihty introduced by the sampling and analytical error is smah, even for those methods such as asbestos counting, which are relatively imprecise. 

Here again the quantity is the (1 — /3) percentile of a chi square distribution with V degrees of freedom. If only a 100(1 — a)% lower confidence limit is desired, it can be calculated from... 

D. I. Gibbons and L. C. Vance, M Simulation Study of Estimators for the Parameters and Percentiles in the Two-Parameter Weibull Distribution, General Motors Research Publication No. GMR-3041, General Motors, Detroit, Mich., 1979. 

The median particle diameter is the diameter which divides half of the measured quantity (mass, surface area, number), or divides the area under a frequency curve ia half The median for any distribution takes a different value depending on the measured quantity. The median, a useful measure of central tendency, can be easily estimated, especially when the data are presented ia cumulative form. In this case the median is the diameter corresponding to the fiftieth percentile of the distribution. 

Example 10 Logistics Curve We shall derive the logistics curve representing the ciimiilarive-freqiiency distrihiitions of the normal distrihiition curve defined by Eqs. (9-72) and (9-73). In this case, y varies between a cumulative probability of zero and unity as z varies from — to -l-oo. Since the upper bound is unity, c = 1. From Table 9-10 the area under the right-hand side of the curve between = 0 and z = z may be read. Since the frequency curve is symmetrical about the mean, this is also the area between = 0 and z=z. Hence, the area under the frequency curve, which represents the cumulative probability, is 0.50000 at = 0 and the 80 percentile, for which the area is 0.80000, corresponds to the value = 0.842. We substitute these values into Eqs. (9-92) through (9-94) to give... 

The probabihty-density function for the normal distribution cui ve calculated from Eq. (9-95) by using the values of a, b, and c obtained in Example 10 is also compared with precise values in Table 9-10. In such symmetrical cases the best fit is to be expected when the median or 50 percentile Xm is used in conjunction with the lower quartile or 25 percentile Xl or with the upper quartile or 75 percentile X[j. These statistics are frequently quoted, and determination of values of a, b, and c by using Xm with Xl and with Xu is an indication of the symmetry of the cui ve. When the agreement is reasonable, the mean v ues of o so determined should be used to calculate the corresponding value of a. 

Animal Maximum average /igC /igC 95 percentile figC Maximum figC Annual areraqe figc 95 percentile figC ... 

The relationship of these response curves to ambient air quality is shown by lines A, B, and C, which represent the maximum or any other chose percentile line from a display such as Fig. 4-10, which shows actual air quality. Where the air quality is poor (line A), essentially all the adverse effects displayed will occur. Where the air quality is good (line C), most of the intermediate and long-term adverse effects displayed will not occur. Where the air quality is between good and poor, some of the intermediate and long-term adverse effects will occur, but in an attenuated form compared with those of poor air quality. These concepts will be referred to later in this text when air quality standards are discussed. 

Useful percentiles of the lognormal are given in equations 2.5-12 through 2.5-1, k is the appropriate coefficient found in tables of the normal distribution... 

The error factor (EF) defined as equation 2.5-16 relates the 50th percentile to the 95th percentile (equation 2.5-17) and the 5th percentile (equatin 2.5-18). 

Statistics on the data fields summary statistics (mean, std dev, min, max), percentile values at desired intervals, and linear regression on two numerical data fields. 

Data Input models are achieved through a standardized procedure as single values, custom distributions (normal, lognormal, etc.), distributions based on data files present in THERdbASE, or specific percentile values. Models have relational access to input data files. 

The mean core damage frequency from all internal events is 1.8E-4/yr, with an error factor (95% percentile divided by the median) of 5.0. The percentage contributions to the core dai e frequencies are Large Reactivity Insertion 28% Large LOCA, 28% Reactivity Insertion L P ramp, 12% Spurious/normal shutdown, 11% Loss of commercial power, 10% and others, 5 ... 

Suggest and confirm with customer the outdoor or process conditions within which the target levels must be met (e.g., absolute maximum temperature versus 95 percentile temperature). 

Computerized Aggregate of Reliability Parameters (CARP) A computer code developed by SAIC to aggregate data sets into a single generic set determine uncertainty bounds (5th and 95th percentiles) fit raw data to statistical distributions and print reports documenting determinations made. 

Error factor The ratio of the 95th percentile value to the median value of a lognormal distribution. 

Because the slope factor is often an upper 95 percentile confidence limit of the probability of response based on experimental animal data used in tlie multistage model, tlie carcinogenic risk estimate will generally be an upper-bound estimate. Tliis means tliat tlie EPA is reasonably confident tliat tlie true risk will not exceed the risk estimate derived tlirough use of tliis model and is likely to be less than tliat predicted. 

Mosleh, Kazarians, and Gekler obtained a Bayesian estimate of the failure rate, Z, of a coolant recycle pump in llie hazard/risk study of a chemical plant. The estimate was based on evidence of no failures in 10 years of operation. Nuclear industry experience with pumps of similar types was used to establish tire prior distribution of Z. Tliis experience indicated tliat tire 5 and 95 percentiles of lire failure rate distribution developed for tliis category were 2.0 x 10" per hour (about one failure per 57 years of operation) and 98.3 x 10 per hour (about one failure per year). Extensive experience in other industries suggested the use of a log-nonnal distribution witli tlie 5 and 95 percentile values as llie prior distribution of Z, tlie failure rate of the coolant recycle pump. 

Recall lliat if Z has a log-nonnal distribution, tlien In Z lias a nonnal distribution with mean p and standard deviation g equal to the parameters in tlie pdf of Z. This fact, in conjunction witli tlie specified 5 and 95 percentiles of llie probability distribution of Z, can be used to obtain the values of p and a, and tliereby the parameters of tlie log-nonnal pdf of Z. If Z denotes the failure rate per year, tlie fact tliat tlie 5" percentile of the distribution of Z is 1/57 implies... 

The fact tliat tlie 95 percentile of the distribution of Z is 1 implies... 

The 5 percentile Poos tuid Uie 95 percentile P095 of tlie posterior distribution of z are defined by... 

Comparison of the 5" and 95 percentiles of the posterior distribution of Z with the 5 and 95 percentiles of the prior distribution of Z indicates tliat the posterior pdf lies to the left of the prior pdf. Therefore, the posterior pdf assigns higher probability to intervals in the lower part of the range of z than the prior pdf. Tliis reflects the influence of tlie observed occurrence of no failures in 10 years. 

All the previous discussions have concerned steady-state noise. It will, however, be apparent that most noises change in level with time. It may therefore be necessary to derive indices which describe how this happens. The most common of these are percentiles and equivalent continuous noise levels. 

Percentiles are expressed as the percentage of time (for the stated period) during which the stated noise level was exceeded, i.e. 5 min Lgo of 80 dB(A) means that for the 5-min period of measurement for 90 per cent of the time the noise exceeded 80dB(A). Therefore Lo is the maximum noise level during any period and Lioo is the minimum. Leq (the equivalent continuous noise level) is the level which, if it were constant for the stated period, would have the same amount of acoustic energy as the actual varying noise level. 

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