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Module « scipy.stats »

Fonction yeojohnson - module scipy.stats

Signature de la fonction yeojohnson

def yeojohnson(x, lmbda=None) 

Description

help(scipy.stats.yeojohnson)

Return a dataset transformed by a Yeo-Johnson power transformation.

Parameters
----------
x : ndarray
    Input array.  Should be 1-dimensional.
lmbda : float, optional
    If ``lmbda`` is ``None``, find the lambda that maximizes the
    log-likelihood function and return it as the second output argument.
    Otherwise the transformation is done for the given value.

Returns
-------
yeojohnson: ndarray
    Yeo-Johnson power transformed array.
maxlog : float, optional
    If the `lmbda` parameter is None, the second returned argument is
    the lambda that maximizes the log-likelihood function.

See Also
--------
probplot, yeojohnson_normplot, yeojohnson_normmax, yeojohnson_llf, boxcox

Notes
-----
The Yeo-Johnson transform is given by::

    y = ((x + 1)**lmbda - 1) / lmbda,                for x >= 0, lmbda != 0
        log(x + 1),                                  for x >= 0, lmbda = 0
        -((-x + 1)**(2 - lmbda) - 1) / (2 - lmbda),  for x < 0, lmbda != 2
        -log(-x + 1),                                for x < 0, lmbda = 2

Unlike `boxcox`, `yeojohnson` does not require the input data to be
positive.

.. versionadded:: 1.2.0


References
----------
I. Yeo and R.A. Johnson, "A New Family of Power Transformations to
Improve Normality or Symmetry", Biometrika 87.4 (2000):


Examples
--------
>>> from scipy import stats
>>> import matplotlib.pyplot as plt

We generate some random variates from a non-normal distribution and make a
probability plot for it, to show it is non-normal in the tails:

>>> fig = plt.figure()
>>> ax1 = fig.add_subplot(211)
>>> x = stats.loggamma.rvs(5, size=500) + 5
>>> prob = stats.probplot(x, dist=stats.norm, plot=ax1)
>>> ax1.set_xlabel('')
>>> ax1.set_title('Probplot against normal distribution')

We now use `yeojohnson` to transform the data so it's closest to normal:

>>> ax2 = fig.add_subplot(212)
>>> xt, lmbda = stats.yeojohnson(x)
>>> prob = stats.probplot(xt, dist=stats.norm, plot=ax2)
>>> ax2.set_title('Probplot after Yeo-Johnson transformation')

>>> plt.show()

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