Percentile estimates

Rice S, Church M (1996) Sampling surficial fluvial gravels the precision of size distribution percentile estimates. J Sedimentary Res 66(3) 654—665... 

Then estimate the 0,90 confidence interval of each reference limit from the distribution of the percentile estimates. 

Percentile estimate with respect to a positive reference serum Non-parametric methods are preferable for the estimation... 

Filloon TG (1995) Estimating the minimum therapeutically effective dose of a compound via regression modelling and percentile estimation. Statistics in Medicine 14 925-932 discussion 933. 

It would appear reasonable to assume that the upside and downside information regarding demand implies that the probabilities are well-centered around the mean of 10,000. Therefore, let us assume that demand follows a normal distribution. We can interpret the statement from Marketing to mean that the cumulative probability of demand equaling 14,000 units is 0.90. Thus, we can use a normal look-up table (perhaps the one embedded in the popular Excel spreadsheet software) and use this 90th-percentile estimate from Marketing to compute the standard deviation of our demand distribution. Specifically,... 

This quantity may be interpreted as an adjusted exceedance probability which applies to the reduced sample. When > 0 it is easy to see that we always have p p. A consequence of this is that the percentile estimates becomes more stable as the exceedance events occur much more frequent within the reduced sample. Working with this adjusted exceedance probability also has the technical advantage that we may use exactly the same algorithm for the reduced sample as we use for the full sample except that we replace by ... 

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. 

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. 

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. 

The line the data supports on a hazard plot determines engineering information relating to the distribution of time to failure. Fan failure data and simulated data are illustrated here to explain how the information is obtained. The methods provide estimates of distribution parameters, percentiles, and probabilities of failure. The methods that give estimates of distribution parameters differ slightly from the hazard paper of one theoretical distribution to another and are given separately for each distribution. The methods that give estimates of distribution percentiles and failure probabilities are the same for all papers and are given first. 

Suppose, for example, that an estimate based on a Wei-bull fit to the fan data is desired of the fifth percentile of the distribution of time to fan failure. Enter the Weibull plot. Figure 62.6, on the probability scale at the chosen percentage point, 5 per cent. Go vertically down to the fitted line and then horizontally to the time scale where the estimate of the percentile is read and is 14,000 hours. 

When a set of data does not plot as a straight line on any of the available papers, then one may wish to draw a smooth curve through the data points on one of the plotting papers, and use the curve to obtain estimates of distribution percentiles and probabilities of failure for various given times. With such a nonparametric fit to the data, it is usually unsatisfactory to extrapolate beyond the data because it is difficult to determine how to extend how to extend the curve. Nonparametric fitting is best used only if the data contain a reasonably large number of failures. 

Dietary intake data from a number of studies in North America and the United Kingdom indicate that intake of lutein from natural sources is in the range of 1 to 2 mg/day (approximately 0.01 to 0.03 mg/kg body weight per day). Simulations considering proposed levels of use as a food ingredient resulted in an estimated mean and 90th percentile of intake of lutein plus zeaxanthin of approximately 7 and 13 mg/day, respectively. Formulations containing lutein and zeaxanthin are also available as dietary supplements, but no reliable estimates of intakes from these sources were available. 

The target number of commodity samples to be obtained in the OPMBS was 500, as determined using statistical techniques. A sample size of 500 provided at least 95% confidence that the 99th percentile of the population of residues was less than the maximum residue value observed in the survey. In other words, a sample size of 500 was necessary to estimate the upper limit of the 95% confidence interval around the 99th percentile of the population of residues. 

The sample size of the survey will depend primarily on the need to accurately estimate the upper percentiles of the national distribution and the number of subgroup populations for which frequency distributions are needed and the level of accuracy needed for these distributions (Cox et el., 1985). 

If, however, the radon level exceeded by 0.1% of the housing unit is desired, this would require a sample size of 200,000 housing units. These sample sizes could be reduced to 5,000 and 50,0000 units respectively, if a RSE of 20% were considered adequate. A design effect of 2 was used in estimating these sample sizes. Table 1 shows the sample sizes as a function of both percentile of interest and precision of the estimates. 

These estimates are for a national distribution and will increase depending upon the number of subpopulation groups for which frequency distribution data is desired. Determining the sample size, therefore, requires decisions regarding the percentile of interest and level of accuracy needed, and balancing these against the costs of the required sample. 

In 2005, the EES A [62] made an estimation of PAE exposure in human populations based on the limited available literature on DEHP, DBP, BBP, DiNP, and DiDP concentration in foods and diets. Some studies have been conducted in two different populations in United Kingdom (UK) and Denmark from 1996 to 2003 [124—129]. Based on the information obtained from the mentioned studies, the EFSA estimated the daily oral intake and the maximum dietary exposure (calculated in the 95th percentile) (MDE) for the most used PAEs (Table 3). 

Table 3 Estimation of maximum dietary exposure (MDE) (95th percentile), non observed adverse effect level (NOAEL) and tolerable dally Intake (TDI) of the most used PAEs according to EFSA [62]...

The EDI of phthalates in China, Germany, Taiwan, and US populations are shown in Table 7. The calculation was based on phthalate metabolite (primary and secondary) concentrations, the model of David [137] and the excretion fractions according to various authors [23,28,143,144]. DEHP median values are very close or clearly exceed the TDIs and RfD values (Table 4). The median values for the rest of PAEs are below levels determined to be safe for daily exposures estimated by the US (RfD), the EU and Japan (TDI) (Table 4). However, the upper percentiles of DBP and DEHP urinary metabolite concentrations suggested that for some people, these daily phthalate intakes might be substantially higher than previously assumed and exceed the RfD and TDIs. 

Table 7 Estimated daily intakes of phthalates in different countries, median (range or 95th percentile), based in urinary metabolite concentrations, expressed in pg/kg b.w./day... 

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