atoti.array.quantile module

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:

• 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 (MeasureDescription) – The measure to get the quantile of.

• q (Union[float, MeasureDescription]) – The quantile to take. Must be between 0 and 1. For instance, 0.95 is the 95th percentile and 0.5 is the median.

• mode (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[‘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

MeasureDescription