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# scipy.stats.yeojohnson

scipy.stats.yeojohnson(x, lmbda=None)

  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.

  New in version 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()