`scipy.stats._morestats:yeojohnson`

source: /scipy/stats/_morestats.py :1574

Signature

def yeojohnson ( x , lmbda = None )

Summary

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.

Notes

The Yeo-Johnson transform is given by:

y = ⎩ ⎨ ⎧ \frac{( x + 1 ) ^{λ} - 1}{λ}, lo g (x + 1), - \frac{( - x + 1 ) ^{2 - λ} - 1}{2 - λ}, - lo g (- x + 1), for x \geq 0, λ \neq = 0 for x \geq 0, λ = 0 for x < 0, λ \neq = 2 for x < 0, λ = 2

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

Array API Standard Support

yeojohnson has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ⛔                   
PyTorch               ⛔                     ⛔                   
JAX                   ⛔                     ⛔                   
Dask                  ⛔                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

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()

✓

Aliases

scipy.stats.yeojohnson