Using PowerTransformer to apply the Box-Cox transformationΒΆ

This example demonstrates the use of the Box-Cox transform through preprocessing.PowerTransformer to map data from various distributions to a normal distribution.

Box-Cox is useful as a transformation in modeling problems where homoscedasticity and normality are desired. Below are examples of Box-Cox applied to six different probability distributions: Lognormal, Chi-squared, Weibull, Gaussian, Uniform, and Bimodal.

Note that the transformation successfully maps the data to a normal distribution when applied to certain datasets, but is ineffective with others. This highlights the importance of visualizing the data before and after transformation. Also note that while the standardize option is set to False for the plot examples, by default, preprocessing.PowerTransformer also applies zero-mean, unit-variance standardization to the transformed outputs.

# Author: Eric Chang <>
# License: BSD 3 clause

import numpy as np
import matplotlib.pyplot as plt

from sklearn.preprocessing import PowerTransformer, minmax_scale


N_SAMPLES = 3000
BINS = 100

pt = PowerTransformer(method='box-cox', standardize=False)
rng = np.random.RandomState(304)
size = (N_SAMPLES, 1)

# lognormal distribution
X_lognormal = rng.lognormal(size=size)

# chi-squared distribution
df = 3
X_chisq = rng.chisquare(df=df, size=size)

# weibull distribution
a = 50
X_weibull = rng.weibull(a=a, size=size)

# gaussian distribution
loc = 100
X_gaussian = rng.normal(loc=loc, size=size)

# uniform distribution
X_uniform = rng.uniform(low=0, high=1, size=size)

# bimodal distribution
loc_a, loc_b = 100, 105
X_a, X_b = rng.normal(loc=loc_a, size=size), rng.normal(loc=loc_b, size=size)
X_bimodal = np.concatenate([X_a, X_b], axis=0)

# create plots
distributions = [
    ('Lognormal', X_lognormal),
    ('Chi-squared', X_chisq),
    ('Weibull', X_weibull),
    ('Gaussian', X_gaussian),
    ('Uniform', X_uniform),
    ('Bimodal', X_bimodal)

colors = ['firebrick', 'darkorange', 'goldenrod',
          'seagreen', 'royalblue', 'darkorchid']

fig, axes = plt.subplots(nrows=4, ncols=3)
axes = axes.flatten()
axes_idxs = [(0, 3), (1, 4), (2, 5), (6, 9), (7, 10), (8, 11)]
axes_list = [(axes[i], axes[j]) for i, j in axes_idxs]

for distribution, color, axes in zip(distributions, colors, axes_list):
    name, X = distribution
    # scale all distributions to the range [0, 10]
    X = minmax_scale(X, feature_range=(1e-10, 10))

    # perform power transform
    X_trans = pt.fit_transform(X)
    lmbda = round(pt.lambdas_[0], 2)

    ax_original, ax_trans = axes

    ax_original.hist(X, color=color, bins=BINS)
    ax_original.set_title(name, fontsize=FONT_SIZE)
    ax_original.tick_params(axis='both', which='major', labelsize=FONT_SIZE)

    ax_trans.hist(X_trans, color=color, bins=BINS)
    ax_trans.set_title('{} after Box-Cox, $\lambda$ = {}'.format(name, lmbda),
    ax_trans.tick_params(axis='both', which='major', labelsize=FONT_SIZE)


Total running time of the script: ( 0 minutes 1.479 seconds)

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