SciPy

numpy.nanvar

numpy.nanvar(a, axis=None, dtype=None, out=None, ddof=0, keepdims=<class numpy._NoValue at 0x40a1fe3c>)[source]

Compute the variance along the specified axis, while ignoring NaNs.

Returns the variance of the array elements, a measure of the spread of a distribution. The variance is computed for the flattened array by default, otherwise over the specified axis.

For all-NaN slices or slices with zero degrees of freedom, NaN is returned and a RuntimeWarning is raised.

New in version 1.8.0.

Parameters:

a : array_like

Array containing numbers whose variance is desired. If a is not an array, a conversion is attempted.

axis : int, optional

Axis along which the variance is computed. The default is to compute the variance of the flattened array.

dtype : data-type, optional

Type to use in computing the variance. For arrays of integer type the default is float32; for arrays of float types it is the same as the array type.

out : ndarray, optional

Alternate output array in which to place the result. It must have the same shape as the expected output, but the type is cast if necessary.

ddof : int, optional

“Delta Degrees of Freedom”: the divisor used in the calculation is N - ddof, where N represents the number of non-NaN elements. By default ddof is zero.

keepdims : bool, optional

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 original a.

Returns:

variance : ndarray, see dtype parameter above

If out is None, return a new array containing the variance, otherwise return a reference to the output array. If ddof is >= the number of non-NaN elements in a slice or the slice contains only NaNs, then the result for that slice is NaN.

See also

std
Standard deviation
mean
Average
var
Variance while not ignoring NaNs

nanstd, nanmean

numpy.doc.ufuncs
Section “Output arguments”

Notes

The variance is the average of the squared deviations from the mean, i.e., var = mean(abs(x - x.mean())**2).

The mean is normally calculated as x.sum() / N, where N = len(x). If, however, ddof is specified, the divisor N - ddof is used instead. In standard statistical practice, ddof=1 provides an unbiased estimator of the variance of a hypothetical infinite population. ddof=0 provides a maximum likelihood estimate of the variance for normally distributed variables.

Note that for complex numbers, the absolute value is taken before squaring, so that the result is always real and nonnegative.

For floating-point input, the variance is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for float32 (see example below). Specifying a higher-accuracy accumulator using the dtype keyword can alleviate this issue.

For this function to work on sub-classes of ndarray, they must define sum with the kwarg keepdims

Examples

>>> a = np.array([[1, np.nan], [3, 4]])
>>> np.var(a)
1.5555555555555554
>>> np.nanvar(a, axis=0)
array([ 1.,  0.])
>>> np.nanvar(a, axis=1)
array([ 0.,  0.25])

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