scipy.stats.boxcox_normplot(x, la, lb, plot=None, N=80)[source]

Compute parameters for a Box-Cox normality plot, optionally show it.

A Box-Cox normality plot shows graphically what the best transformation parameter is to use in boxcox to obtain a distribution that is close to normal.


Input array.

la, lbscalar

The lower and upper bounds for the lmbda values to pass to boxcox for Box-Cox transformations. These are also the limits of the horizontal axis of the plot if that is generated.

plotobject, optional

If given, plots the quantiles and least squares fit. plot is an object that has to have methods “plot” and “text”. The matplotlib.pyplot module or a Matplotlib Axes object can be used, or a custom object with the same methods. Default is None, which means that no plot is created.

Nint, optional

Number of points on the horizontal axis (equally distributed from la to lb).


The lmbda values for which a Box-Cox transform was done.


Probability Plot Correlelation Coefficient, as obtained from probplot when fitting the Box-Cox transformed input x against a normal distribution.


Even if plot is given, the figure is not shown or saved by boxcox_normplot; or plt.savefig('figname.png') should be used after calling probplot.


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

Generate some non-normally distributed data, and create a Box-Cox plot:

>>> x = stats.loggamma.rvs(5, size=500) + 5
>>> fig = plt.figure()
>>> ax = fig.add_subplot(111)
>>> prob = stats.boxcox_normplot(x, -20, 20, plot=ax)

Determine and plot the optimal lmbda to transform x and plot it in the same plot:

>>> _, maxlog = stats.boxcox(x)
>>> ax.axvline(maxlog, color='r')