gmean#
- scipy.stats.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, aValueError
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 tonp.ndarray
before the calculation is performed. In this case, the output will be a scalar ornp.ndarray
of appropriate shape rather than a 2Dnp.matrix
. Similarly, while masked elements of masked arrays are ignored, the output will be a scalar ornp.ndarray
rather than a masked array withmask=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