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Private version of `variation` that ignores nan.
`a` must be a numpy array.
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Compute the coefficient of variation.
The coefficient of variation is the standard deviation divided by the
mean. This function is equivalent to::
np.std(x, axis=axis, ddof=ddof) / np.mean(x)
The default for ``ddof`` is 0, but many definitions of the coefficient
of variation use the square root of the unbiased sample variance
for the sample standard deviation, which corresponds to ``ddof=1``.
The function does not take the absolute value of the mean of the data,
so the return value is negative if the mean is negative.
Parameters
----------
a : array_like
Input array.
axis : int or None, optional
Axis along which to calculate the coefficient of variation.
Default is 0. If None, compute over the whole array `a`.
nan_policy : {'propagate', 'raise', 'omit'}, optional
Defines how to handle when input contains ``nan``.
The following options are available:
* 'propagate': return ``nan``
* 'raise': raise an exception
* 'omit': perform the calculation with ``nan`` values omitted
The default is 'propagate'.
ddof : int, optional
Gives the "Delta Degrees Of Freedom" used when computing the
standard deviation. The divisor used in the calculation of the
standard deviation is ``N - ddof``, where ``N`` is the number of
elements. `ddof` must be less than ``N``; if it isn't, the result
will be ``nan`` or ``inf``, depending on ``N`` and the values in
the array. By default `ddof` is zero for backwards compatibility,
but it is recommended to use ``ddof=1`` to ensure that the sample
standard deviation is computed as the square root of the unbiased
sample variance.
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 input array.
Returns
-------
variation : ndarray
The calculated variation along the requested axis.
Notes
-----
There are several edge cases that are handled without generating a
warning:
* If both the mean and the standard deviation are zero, ``nan``
is returned.
* If the mean is zero and the standard deviation is nonzero, ``inf``
is returned.
* If the input has length zero (either because the array has zero
length, or all the input values are ``nan`` and ``nan_policy`` is
``'omit'``), ``nan`` is returned.
* If the input contains ``inf``, ``nan`` is returned.
References
----------
.. [1] Zwillinger, D. and Kokoska, S. (2000). CRC Standard
Probability and Statistics Tables and Formulae. Chapman & Hall: New
York. 2000.
Examples
--------
>>> import numpy as np
>>> from scipy.stats import variation
>>> variation([1, 2, 3, 4, 5], ddof=1)
0.5270462766947299
Compute the variation along a given dimension of an array that contains
a few ``nan`` values:
>>> x = np.array([[ 10.0, np.nan, 11.0, 19.0, 23.0, 29.0, 98.0],
... [ 29.0, 30.0, 32.0, 33.0, 35.0, 56.0, 57.0],
... [np.nan, np.nan, 12.0, 13.0, 16.0, 16.0, 17.0]])
>>> variation(x, axis=1, ddof=1, nan_policy='omit')
array([1.05109361, 0.31428986, 0.146483 ])
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