Percentile, defined

The 85th percentile, defining those who are at risk for becoming obese. 

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 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). 

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

The second new program allows the user to compare the shapes of molecular weight distributions. For example, if we have the cumulative distribution of hydrodynamic volume for two polymers we can plot the hydrodynamic volume corresponding to the 10th percentile of the distribution for polymer A against the similarly defined hydrodynamic volume for polymer B. Such a plot, made for the entire distribution of both polymers, is called a "quantile... 

Figure 1.8 explains graphically how probabilities and quantiles are defined for a normal distribution. For instance the 1 %-percentile (p = 0.01) of the standard normal distribution is —2.326, and the 99%-percentile (p 0.99) is 2.326 both together define a 98% interval. 

Reanalysis of the data of Hattis et al. (1987) showed that the variation between individuals for the elimination half-life was quite small (Schaddelee 1997, as cited in Vermeire et al. 1999, 2001). Defining the interindividual factor as the ratio of the P50 (50th percentile) and P05 (5th percentile) resulted in a factor of 1.4. It was emphasized that although it appeared from this analysis that a 10-fold factor would be sufficient for pharmacokinetic variation, the real median to sensitive human variability is underestimated because variation also exists in pharmacodynamics and only data of healthy volunteers were available. 

The hypothesis to be tested requires an appropriate test statistic. Since acute toxins are being considered here, it is essential to choose a statistical measure that is likely to identify lognormal distributions that potentially produce large values, even if these values are improbable. A sensitive statistic tic must combine both the overall level (mean) and the intrinsic variability (variance). A test statistic with this property is the estimated 95th percentile defined as... 

Note Values are the volume of tap water consumed in Canada per person per day, in liters. a The range is defined by die 10th and 90th percentiles for each age group. 

Points 1 to 3 explicitly define the assessment of compliance. Point 1 is what many scientists would regard as the standard, but it is only a part of the standard. Points 2 and 3 deal with the requirement that the limit value needs to be used for 2 purposes to estimate the measures needed to correct or prevent failure and to assess compliance in an unbiased manner (perhaps in a way that enables comparisons between regions or nations). Both of these tasks require standards defined as summary statistics that can be estimated using statistical methods in an unbiased manner, thus allowing the quantification of statistical errors. Generally, this means that the standards must be expressed as summary statistics such as annual averages and annual percentiles. 

An additional problem lies in setting up the action to secure compliance. An absolute limit must never be exceeded, but what is meant by never Once in a million years The answer to this question defines the absolute limit as a percentile it expresses the proportion of time for which failure is acceptable. This is also the outcome when we select a sampling frequency. There are 31 million seconds in a year, and we might sample 12 of them. This leaves a lot of time when we might fail the absolute limit and not notice it, and this accepted proportion of time defines the percentile Twelve samples a year treats an absolute limit as something like an annual 95th percentile. 

The statistical process sets up a sampling protocol that is constructed to provide an unbiased estimate of the summary statistic that defines the standard, say the annual mean or annual 95th percentile. The statistical methods provide an estimate of the standard error about this estimate of the summary statistic. Usually, the sampling regime... 

A maximal concentration of cTnl or cTnl exceeding the decision limit, defined as the 99th percentile of values for a reference control group, on at least one occasion during the first 24 hours after the index clinical event. 

Final results are given as percentile fraction unbound (fu) of percentile fraction bound (fb) for a defined concentration. 

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