pmean#
- scipy.stats.pmean(a, p, *, axis=0, dtype=None, weights=None, nan_policy='propagate', keepdims=False)[source]#
- Calculate the weighted power mean along the specified axis. - The weighted power mean of the array \(a_i\) associated to weights \(w_i\) is: \[\left( \frac{ \sum_{i=1}^n w_i a_i^p }{ \sum_{i=1}^n w_i } \right)^{ 1 / p } \, ,\]- and, with equal weights, it gives: \[\left( \frac{ 1 }{ n } \sum_{i=1}^n a_i^p \right)^{ 1 / p } \, .\]- When - p=0, it returns the geometric mean.- This mean is also called generalized mean or Hölder mean, and must not be confused with the Kolmogorov generalized mean, also called quasi-arithmetic mean or generalized f-mean [3]. - Parameters:
- aarray_like
- Input array, masked array or object that can be converted to an array. 
- pint or float
- Exponent. 
- 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 of the returned array and of the accumulator in which the elements are summed. If dtype is not specified, it defaults to the dtype of a, unless a has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used. 
- weightsarray_like, optional
- 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. 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- ValueErrorwill 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:
- pmeanndarray, see dtype parameter above.
- Output array containing the power mean values. 
 
 - See also - numpy.average
- Weighted average 
- gmean
- Geometric mean 
- hmean
- Harmonic mean 
 - Notes - The power mean is computed over a single dimension of the input array, - axis=0by default, or all values in the array if- axis=None. float64 intermediate and return values are used for integer inputs.- The power mean is only defined if all observations are non-negative; otherwise, the result is NaN. - Added in version 1.9. - Beginning in SciPy 1.9, - np.matrixinputs (not recommended for new code) are converted to- np.ndarraybefore the calculation is performed. In this case, the output will be a scalar or- np.ndarrayof 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.ndarrayrather than a masked array with- mask=False.- pmeanhas 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=1and 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 - ⚠️ no JIT - ⚠️ no JIT - Dask - ⚠️ computes graph - n/a - See Support for the array API standard for more information. - References [1]- “Generalized Mean”, Wikipedia, https://en.wikipedia.org/wiki/Generalized_mean [2]- Norris, N., “Convexity properties of generalized mean value functions”, The Annals of Mathematical Statistics, vol. 8, pp. 118-120, 1937 [3]- Bullen, P.S., Handbook of Means and Their Inequalities, 2003 - Examples - >>> from scipy.stats import pmean, hmean, gmean >>> pmean([1, 4], 1.3) 2.639372938300652 >>> pmean([1, 2, 3, 4, 5, 6, 7], 1.3) 4.157111214492084 >>> pmean([1, 4, 7], -2, weights=[3, 1, 3]) 1.4969684896631954 - For p=-1, power mean is equal to harmonic mean: - >>> pmean([1, 4, 7], -1, weights=[3, 1, 3]) 1.9029126213592233 >>> hmean([1, 4, 7], weights=[3, 1, 3]) 1.9029126213592233 - For p=0, power mean is defined as the geometric mean: - >>> pmean([1, 4, 7], 0, weights=[3, 1, 3]) 2.80668351922014 >>> gmean([1, 4, 7], weights=[3, 1, 3]) 2.80668351922014