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# numpy.percentile

numpy.percentile(a, q, axis=None, out=None, overwrite_input=False, method='linear', keepdims=False, *, weights=None)

  Compute the q-th percentile of the data along the specified axis.

  Returns the q-th percentile(s) of the array elements.

  Parameters:
    a array_like of real numbers

      Input array or object that can be converted to an array.

    q array_like of float

      Percentage or sequence of percentages for the percentiles to compute. Values must be between 0 and 100 inclusive.

    axis{int, tuple of int, None}, optional

      Axis or axes along which the percentiles are computed. The default is to compute the percentile(s) along a flattened version of the array.

    out ndarray, optional

      Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type (of the output) will be cast if necessary.

    overwrite_input bool, optional

      If True, then allow the input array a to be modified by intermediate calculations, to save memory. In this case, the contents of the input a after this function completes is undefined.

    method str, optional

      This parameter specifies the method to use for estimating the percentile. There are many different methods, some unique to NumPy. See the notes for explanation. The options sorted by their R type as summarized in the H&F paper [1] are:

      1. ‘inverted_cdf’

      2. ‘averaged_inverted_cdf’

      3. ‘closest_observation’

      4. ‘interpolated_inverted_cdf’

      5. ‘hazen’

      6. ‘weibull’

      7. ‘linear’ (default)

      8. ‘median_unbiased’

      9. ‘normal_unbiased’

      The first three methods are discontinuous. NumPy further defines the following discontinuous variations of the default ‘linear’ (7.) option:

      - ‘lower’

      - ‘higher’,

      - ‘midpoint’

      - ‘nearest’

      Changed in version 1.22.0: This argument was previously called “interpolation” and only offered the “linear” default and last four options.

    keepdims bool, optional

      If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original array a.

    weights array_like, optional

      An array of weights associated with the values in a. Each value in a contributes to the percentile according to its associated weight. The weights array can either be 1-D (in which case its length must be the size of a along the given axis) or of the same shape as a. If weights=None, then all data in a are assumed to have a weight equal to one. Only method=”inverted_cdf” supports weights. See the notes for more details.

      New in version 2.0.0.

  Returns:
    percentile scalar or ndarray

      If q is a single percentile and axis=None, then the result is a scalar. If multiple percentiles are given, first axis of the result corresponds to the percentiles. The other axes are the axes that remain after the reduction of a. If the input contains integers or floats smaller than `float64`, the output data-type is `float64`. Otherwise, the output data-type is the same as that of the input. If out is specified, that array is returned instead.

  See also

  `mean`
  `median`

    equivalent to `percentile(..., 50)`

  `nanpercentile`
  `quantile`

    equivalent to percentile, except q in the range [0, 1].

  Notes

  The behavior of `numpy.percentile` with percentage q is that of `numpy.quantile` with argument `q/100`. For more information, please see `numpy.quantile`.

  References

  [1]

  R. J. Hyndman and Y. Fan, “Sample quantiles in statistical packages,” The American Statistician, 50(4), pp. 361-365, 1996

  Examples

      >>> import numpy as np
      >>> a = np.array([[10, 7, 4], [3, 2, 1]])
      >>> a
      array([[10,  7,  4],
             [ 3,  2,  1]])
      >>> np.percentile(a, 50)
      3.5
      >>> np.percentile(a, 50, axis=0)
      array([6.5, 4.5, 2.5])
      >>> np.percentile(a, 50, axis=1)
      array([7.,  2.])
      >>> np.percentile(a, 50, axis=1, keepdims=True)
      array([[7.],
             [2.]])

      >>> m = np.percentile(a, 50, axis=0)
      >>> out = np.zeros_like(m)
      >>> np.percentile(a, 50, axis=0, out=out)
      array([6.5, 4.5, 2.5])
      >>> m
      array([6.5, 4.5, 2.5])

      >>> b = a.copy()
      >>> np.percentile(b, 50, axis=1, overwrite_input=True)
      array([7.,  2.])
      >>> assert not np.all(a == b)

  The different methods can be visualized graphically:

      import matplotlib.pyplot as plt

      a = np.arange(4)
      p = np.linspace(0, 100, 6001)
      ax = plt.gca()
      lines = [
          ('linear', '-', 'C0'),
          ('inverted_cdf', ':', 'C1'),
          # Almost the same as `inverted_cdf`:
          ('averaged_inverted_cdf', '-.', 'C1'),
          ('closest_observation', ':', 'C2'),
          ('interpolated_inverted_cdf', '--', 'C1'),
          ('hazen', '--', 'C3'),
          ('weibull', '-.', 'C4'),
          ('median_unbiased', '--', 'C5'),
          ('normal_unbiased', '-.', 'C6'),
          ]
      for method, style, color in lines:
          ax.plot(
              p, np.percentile(a, p, method=method),
              label=method, linestyle=style, color=color)
      ax.set(
          title='Percentiles for different methods and data: ' + str(a),
          xlabel='Percentile',
          ylabel='Estimated percentile value',
          yticks=a)
      ax.legend(bbox_to_anchor=(1.03, 1))
      plt.tight_layout()
      plt.show()