Repository: scikit-learn/scikit-learn
File: sklearn/utils/stats.py (Python)

Code before:
def _weighted_percentile(
    array, sample_weight, percentile_rank=50, average=False, xp=None
):
    """Compute the weighted percentile.

    Implement an array API compatible (weighted version) of NumPy's 'inverted_cdf'
    method when `average=False` (default) and 'averaged_inverted_cdf' when
    `average=True`.

    For an array ordered by increasing values, when the percentile lies exactly on a
    data point:
    * 'inverted_cdf' takes the exact data point
    * 'averaged_inverted_cdf' takes the average of the exact data point and the one
      above it (this means it gives the same result as `median` for unit weights)
    E.g., for the array [1, 2, 3, 4] the percentile rank at each data point would
    be [25, 50, 75, 100]. Percentile rank 50 lies on '2'. 'average_inverted_cdf'
    takes the average of '2' and '3' makes it 'symmetrical' because if you
    reverse the array, rank 50 would fall on '3'. It also matches 'median'.
    inverted_cdf', which does not satisfy the symmetry property, would give '2'.

    When the percentile lies between two data points, both methods take the higher
    data point.
    E.g., for the array [1, 2, 3, 4, 5] the percentile rank at each data point would
    be [20, 40, 60, 80, 100]. Percentile rank 50, lies between '2' and '3'. Taking the
    higher data point is symmetrical because if you reverse the array, 50 would lie
    between '4' and '3'. Both methods match median in this case.

    If `array` is a 2D array, the `values` are selected along axis 0.

    `NaN` values are ignored by setting their weights to 0. If `array` is 2D, this
    is done in a column-isolated manner: a `NaN` in the second column, does not impact
    the percentile computed for the first column even if `sample_weight` is 1D.

        .. versionchanged:: 0.24
            Accepts 2D `array`.

        .. versionchanged:: 1.7
            Supports handling of `NaN` values.

        .. versionchanged:: 1.8
            Supports `average`, which calculates percentile using
            "averaged_inverted_cdf" method.

    Parameters
    ----------
    array : 1D or 2D array
        Values to take the weighted percentile of.

    sample_weight: 1D or 2D array
        Weights for each value in `array`. Must be same shape as `array` or of shape
        `(array.shape[0],)`.

Review comment (suggestion):
I have given an example and an intuition on symmetry for both.

I did not go into the calculation for `g` because I don't think it is necessary...

Code after:
def _weighted_percentile(
    array, sample_weight, percentile_rank=50, average=False, xp=None
):
    """Compute the weighted percentile.

    Implement an array API compatible (weighted version) of NumPy's 'inverted_cdf'
    method when `average=False` (default) and 'averaged_inverted_cdf' when
    `average=True`.

    For an array ordered by increasing values, when the percentile lies exactly on a
    data point:

    * 'inverted_cdf' takes the exact data point.
    * 'averaged_inverted_cdf' takes the average of the exact data point and the one
      above it (this means it gives the same result as `median` for unit weights).

    E.g., for the array [1, 2, 3, 4] the percentile rank at each data point would
    be [25, 50, 75, 100]. Percentile rank 50 lies on '2'. 'average_inverted_cdf'
    computes the average of '2' and '3', making it 'symmetrical' because if you
    reverse the array, rank 50 would fall on '3'. It also matches 'median'.
    On the other hand, 'inverted_cdf', which does not satisfy the symmetry property,
    would give '2'.

    When the requested percentile lies between two data points, both methods return
    the higher data point.
    E.g., for the array [1, 2, 3, 4, 5] the percentile rank at each data point would
    be [20, 40, 60, 80, 100]. Percentile rank 50, lies between '2' and '3'. Taking the
    higher data point is symmetrical because if you reverse the array, 50 would lie
    between '4' and '3'. Both methods match median in this case.

    If `array` is a 2D array, the `values` are selected along axis 0.

    `NaN` values are ignored by setting their weights to 0. If `array` is 2D, this
    is done in a column-isolated manner: a `NaN` in the second column, does not impact
    the percentile computed for the first column even if `sample_weight` is 1D.

        .. versionchanged:: 0.24
            Accepts 2D `array`.

        .. versionchanged:: 1.7
            Supports handling of `NaN` values.

        .. versionchanged:: 1.8
            Supports `average`, which calculates percentile using the
            "averaged_inverted_cdf" method.

    Parameters
    ----------
    array : 1D or 2D array
        Values to take the weighted percentile of.