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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 (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 [ ‘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: MeasureDefinition