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atoti.array.quantile(
    measure: VariableMeasureConvertible,
    /,
    q: _Quantile,
    *,
    mode: Literal[‘simple’, ‘centered’, ‘inc’, ‘exc’] = 'inc',
    interpolation: Literal[‘linear’, ‘higher’, ‘lower’, ‘nearest’, ‘midpoint’] = 'linear',
) → MeasureDefinition
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.

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Parameters

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measure

The measure to get the quantile of.

​
q

The quantile to take. For instance, 0.95 is the 95th percentile and 0.5 is the median.

​
mode

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

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