2016.10.04 13:43

- Published by:
- Mladen Rakic
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- votes: 15

Some basic information on quantiles :

In statistics and the theory of probability, **quantiles** are cutpoints dividing the range of a probability distribution
into contiguous intervals with equal probabilities, or dividing the
observations in a sample in the same way. There is one less quantile
than the number of groups created. Thus quartiles
are the three cut points that will divide a dataset into four
equal-size groups (cf. depicted example). Common quantiles have special
names: for instance quartile, decile (creating 10 groups: see below for
more). The groups created are termed halves, thirds, quarters, etc.,
though sometimes the terms for the quantile are used for the groups
created, rather than for the cut points.

*q*-**Quantiles** are values that partition a finite set of values into *q* subsets of (nearly) equal sizes. There are *q* − 1 of the *q*-quantiles, one for each integer *k* satisfying 0 < *k* < *q*. In some cases the value of a quantile may not be uniquely determined, as can be the case for the median
(2-quantile) of a uniform probability distribution on a set of even
size. Quantiles can also be applied to continuous distributions,
providing a way to generalize rank statistics to continuous variables. When the cumulative distribution function of a random variable is known, the *q*-quantiles are the application of the quantile function (the inverse function of the cumulative distribution function) to the values {1/*q*, 2/*q*, …, (*q* − 1)/*q*}.

More information can be found here.

This indicator is constructing "bands" using 3 quantile values.

Translated from Russian by MetaQuotes Software Corp.

Original code: https://www.mql5.com/ru/code/16491

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