scipy.stats.boxcox_normmax(x, brack=(-2.0, 2.0), method='pearsonr')[source]

Compute optimal Box-Cox transform parameter for input data.


x : array_like

Input array.

brack : 2-tuple, optional

The starting interval for a downhill bracket search with optimize.brent. Note that this is in most cases not critical; the final result is allowed to be outside this bracket.

method : str, optional

The method to determine the optimal transform parameter (boxcox lmbda parameter). Options are:

‘pearsonr’ (default)

Maximizes the Pearson correlation coefficient between y = boxcox(x) and the expected values for y if x would be normally-distributed.


Minimizes the log-likelihood boxcox_llf. This is the method used in boxcox.


Use all optimization methods available, and return all results. Useful to compare different methods.


maxlog : float or ndarray

The optimal transform parameter found. An array instead of a scalar for method='all'.


>>> from scipy import stats
>>> import matplotlib.pyplot as plt
>>> np.random.seed(1234)  # make this example reproducible

Generate some data and determine optimal lmbda in various ways:

>>> x = stats.loggamma.rvs(5, size=30) + 5
>>> y, lmax_mle = stats.boxcox(x)
>>> lmax_pearsonr = stats.boxcox_normmax(x)
>>> lmax_mle
>>> lmax_pearsonr
>>> stats.boxcox_normmax(x, method='all')
array([ 7.91667384,  7.17718692])
>>> fig = plt.figure()
>>> ax = fig.add_subplot(111)
>>> prob = stats.boxcox_normplot(x, -10, 10, plot=ax)
>>> ax.axvline(lmax_mle, color='r')
>>> ax.axvline(lmax_pearsonr, color='g', ls='--')

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