scipy.stats.mstats.

gmean#

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

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:
aarray_like

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

axisint 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.

dtypedtype, optional

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

weightsarray_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.

keepdimsbool, 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:
gmeanndarray

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.

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
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