Quantile percentile

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. 

Quantile The value in a distribution that corresponds to a specified proportion of the population distribution or distribution function. Quartiles (25th, 50th, and 75th percentiles), the median (50th percentile), and other percentiles are special cases of quantiles. 

Because (a) is the area in the lower tail of the normal distribution, Za is called the ath quantile of the standard normal distribution, (or the (100)(a)th percentile). A useful identity follows directly from the symmetry of the Gaussian distribution in Equation A-2 (4). 

We have seen that the parameters pg and ag of the lognormal distribution can be estimated by using the 50th percentile and 16th percentile values. These percentiles are called quantiles. Also, (26.36) and (26.37) indicate how this approach can be used to determine the two parameters of the Weibull distribution. 

A quantUe divides a set of observations in two groups, such that one fraction falls above and the complementary fraction below, the value specified by the quantile. The most frequently appUed quantiles are quartiles and percentiles. 

Quantiles can be used for the characterization of the spread of the distribution by giving the distance between the points Xp and Xi p. For instance, the 10-90-percentile range means the difference Xo,g - Xq.i, where Xo,i and Xq,9 are the 10 and the 90 percentile, respectively. It follows from the definition that about 80% of the observed values of X are supposed to lie in this range and about 20% outside. 

Other characteristic size parameters of the distribution function are the percentiles (also quantiles) other than Xso.r- They are commonly used to quantify the... 

Quantile or percentile Xp r is related to the probability p (in percent) that a particle of the distribution is smaller or equal to = p %) ... 

Quantile n An element in the set of location values that divide the set of observations, data sample, population, or probability distribution into groups containing equal numbers of observations. In the case of discrete sets, equal means as equal as possible. There are several common types of quantiles based on the number of groups quartile = four groups, quintile = five groups, decile = ten groups, percentile or centile = one hundred groups. 

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