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scipy.stats.

# gmean

scipy.stats.gmean(a, axis=0, dtype=None, weights=None, *, nan_policy='propagate', keepdims=False)

  Compute the weighted geometric mean along the specified axis.

  The weighted geometric mean of the array \(a_i\) associated to weights \(w_i\) is:

  \[\exp \left( \frac{ \sum_{i=1}^n w_i \ln a_i }{ \sum_{i=1}^n w_i } \right) \, ,\]

  and, with equal weights, it gives:

  \[\sqrt[n]{ \prod_{i=1}^n a_i } \, .\]
  Parameters:
    a array_like

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

    axis int or None, default: 0

      If an int, the axis of the input along which to compute the statistic. The statistic of each axis-slice (e.g. row) of the input will appear in a corresponding element of the output. If `None`, the input will be raveled before computing the statistic.

    dtype dtype, optional

      Type to which the input arrays are cast before the calculation is performed.

    weights array_like, optional

      The weights array must be broadcastable to the same shape as a. Default is None, which gives each value a weight of 1.0.

    nan_policy{‘propagate’, ‘omit’, ‘raise’}

      Defines how to handle input NaNs.

      - `propagate`: if a NaN is present in the axis slice (e.g. row) along which the statistic is computed, the corresponding entry of the output will be NaN.

      - `omit`: NaNs will be omitted when performing the calculation. If insufficient data remains in the axis slice along which the statistic is computed, the corresponding entry of the output will be NaN.

      - `raise`: if a NaN is present, a `ValueError` will be raised.

    keepdims bool, default: False

      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 input array.

  Returns:
    gmean ndarray

      See dtype parameter above.

  See also

  `numpy.mean`

    Arithmetic average

  `numpy.average`

    Weighted average

  `hmean`

    Harmonic mean

  Notes

  The sample geometric mean is the exponential of the mean of the natural logarithms of the observations. Negative observations will produce NaNs in the output because the natural logarithm (as opposed to the complex logarithm) is defined only for non-negative reals.

  Beginning in SciPy 1.9, `np.matrix` inputs (not recommended for new code) are converted to `np.ndarray` before the calculation is performed. In this case, the output will be a scalar or `np.ndarray` of appropriate shape rather than a 2D `np.matrix`. Similarly, while masked elements of masked arrays are ignored, the output will be a scalar or `np.ndarray` rather than a masked array with `mask=False`.

  `gmean` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ✅
  PyTorch | ✅ | ✅
  JAX | ✅ | ✅
  Dask | ✅ | n/a

  See Support for the array API standard for more information.

  References

  [1]

  “Weighted Geometric Mean”, Wikipedia, https://en.wikipedia.org/wiki/Weighted_geometric_mean.

  [2]

  Grossman, J., Grossman, M., Katz, R., “Averages: A New Approach”, Archimedes Foundation, 1983

  Examples

      >>> from scipy.stats import gmean
      >>> gmean([1, 4])
      2.0
      >>> gmean([1, 2, 3, 4, 5, 6, 7])
      3.3800151591412964
      >>> gmean([1, 4, 7], weights=[3, 1, 3])
      2.80668351922014