`scipy.stats._stats_py:gstd`

source: build-install/usr/lib/python3.14/site-packages/scipy/stats/_stats_py.py:2944

Signature

def gstd(a, axis = 0, ddof = 1, *, keepdims = False, nan_policy = propagate)

Summary

Calculate the geometric standard deviation of an array.

Extended Summary

The geometric standard deviation describes the spread of a set of numbers where the geometric mean is preferred. It is a multiplicative factor, and so a dimensionless quantity.

It is defined as the exponential of the standard deviation of the natural logarithms of the observations.

Parameters

a : array_like

An array containing finite, strictly positive, real numbers.

axis : int, tuple or None, optional

Axis along which to operate. Default is 0. If None, compute over the whole array a.

ddof : int, optional

Degree of freedom correction in the calculation of the geometric standard deviation. Default is 1.

keepdims : bool, optional

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

nan_policy : {'propagate', 'omit', 'raise'}, default: 'propagate'

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.

Returns

gstd : ndarray or float: An array of the geometric standard deviation. If axis is None or a is a 1d array a float is returned.

Notes

Mathematically, the sample geometric standard deviation $s_{G}$ can be defined in terms of the natural logarithms of the observations $y_{i} = lo g (x_{i})$ :

s_{G} = exp (s), s = \frac{1}{n - d} i = 1 \sum n (y_{i} - \overset{y}{ˉ})^{2}

where $n$ is the number of observations, $d$ is the adjustment ddof to the degrees of freedom, and $\overset{y}{ˉ}$ denotes the mean of the natural logarithms of the observations. Note that the default ddof=1 is different from the default value used by similar functions, such as numpy.std and numpy.var.

When an observation is infinite, the geometric standard deviation is NaN (undefined). Non-positive observations will also produce NaNs in the output because the natural logarithm (as opposed to the complex logarithm) is defined and finite only for positive reals. The geometric standard deviation is sometimes confused with the exponential of the standard deviation, exp(std(a)). Instead, the geometric standard deviation is exp(std(log(a))).

Examples

Find the geometric standard deviation of a log-normally distributed sample. Note that the standard deviation of the distribution is one; on a log scale this evaluates to approximately ``exp(1)``.

import numpy as np
from scipy.stats import gstd
rng = np.random.default_rng()
sample = rng.lognormal(mean=0, sigma=1, size=1000)

✓

gstd(sample)

✗

np.float64(2.74617412551802)

Compute the geometric standard deviation of a multidimensional array and of a given axis.

a = np.arange(1, 25).reshape(2, 3, 4)

✓

gstd(a, axis=None)
gstd(a, axis=2)
gstd(a, axis=(1,2))

✗

array([2.12939, 1.2212 ])

Aliases

scipy.stats.gstd