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# atoti.array.quantile()

### atoti.array.quantile(measure, /, q, \*, mode='inc', interpolation='linear')

Return a measure equal to the requested quantile of the elements of the passed array measure.

Here is how to obtain the same behavior as [these standard quantile calculation methods](https://en.wikipedia.org/wiki/Quantile#Estimating_quantiles_from_a_sample):

* R-1: `mode="centered"` and `interpolation="lower"`
* R-2: `mode="centered"` and `interpolation="midpoint"`
* R-3: `mode="simple"` and `interpolation="nearest"`
* R-4: `mode="simple"` and `interpolation="linear"`
* R-5: `mode="centered"` and `interpolation="linear"`
* R-6 (similar to Excel’s `PERCENTILE.EXC`): `mode="exc"` and `interpolation="linear"`
* R-7 (similar to Excel’s `PERCENTILE.INC`): `mode="inc"` and `interpolation="linear"`
* R-8 and R-9 are not supported

The formulae given for the calculation of the quantile index assume a 1-based indexing system.

* **Parameters:**
  * **measure** (*VariableMeasureConvertible*) – The measure to get the quantile of.
  * **q** ( *\_Quantile*) – The quantile to take.
    For instance, `0.95` is the 95th percentile and `0.5` is the median.
  * **mode** ([*Literal*](https://docs.python.org/3/library/typing.html#typing.Literal) *\[* *'simple'* *,*  *'centered'* *,*  *'inc'* *,*  *'exc'* *]*) –

    The method used to calculate the index of the quantile.
    Available options are, when searching for the *q* quantile of a vector `X`:

    * `simple`: `len(X) * q`
    * `centered`: `len(X) * q + 0.5`
    * `exc`: `(len(X) + 1) * q`
    * `inc`: `(len(X) - 1) * q + 1`
  * **interpolation** ([*Literal*](https://docs.python.org/3/library/typing.html#typing.Literal) *\[* *'linear'* *,*  *'higher'* *,*  *'lower'* *,*  *'nearest'* *,*  *'midpoint'* *]*) –

    If the quantile index is not an integer, the interpolation decides what value is returned.
    The different options are, considering a quantile index `k` with `i < k < j` for a sorted vector `X`:

    * `linear`: `v = X[i] + (X[j] - X[i]) * (k - i)`
    * `lower`: `v = X[i]`
    * `higher`: `v = X[j]`
    * `nearest`: `v = X[i]` or `v = X[j]` depending on which of `i` or `j` is closest to `k`
    * `midpoint`: `v = (X[i] + X[j]) / 2`
* **Return type:**
  *MeasureDefinition*