## Quantile bands

### Quantile bands

The upper and lower band default is:

- The upper band is 90% quantile
- The lower band is 10% quantile

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*}.

The indicator middle line is not based on the slope of the middle quantile. Instead, it is a combination of the two outer quantiles. When both outer quantiles are showing the same “trend” the color of the middle quantile is the same as the outer quantiles, otherwise, it is “undetermined” (grey, if you use default settings).