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note
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It is worth noting that the problem mentioned arises in more general context, namely within the realm of descriptive statistics. The conventional parametric statistics which is based on momenta estimation often fails to represent adequately the characteristics of nonuniform data and sometimes it leaves the scene in favour to the "nonparametric statistics" As the simplest example, consider the ordinary mean (first momentum) ∫ xp(x)dx of a strongly asymmetric distribution function. Within the nonparametric statistics in order to characterize intuitive notion of the "distribution center" it is common to use the median, or 1/2-quantile instead of the mean value
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