scipy.stats.boxcox_normmax#
- scipy.stats.boxcox_normmax(x, brack=None, method='pearsonr', optimizer=None, *, ymax=BIG_FLOAT)[source]#
Compute optimal Box-Cox transform parameter for input data.
- Parameters:
- xarray_like
Input array. All entries must be positive, finite, real numbers.
- brack2-tuple, optional, default (-2.0, 2.0)
The starting interval for a downhill bracket search for the default optimize.brent solver. Note that this is in most cases not critical; the final result is allowed to be outside this bracket. If optimizer is passed, brack must be None.
- methodstr, 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 fory
if x would be normally-distributed.- ‘mle’
Maximizes the log-likelihood
boxcox_llf
. This is the method used inboxcox
.- ‘all’
Use all optimization methods available, and return all results. Useful to compare different methods.
- optimizercallable, optional
optimizer is a callable that accepts one argument:
- funcallable
The objective function to be minimized. fun accepts one argument, the Box-Cox transform parameter lmbda, and returns the value of the function (e.g., the negative log-likelihood) at the provided argument. The job of optimizer is to find the value of lmbda that minimizes fun.
and returns an object, such as an instance of
scipy.optimize.OptimizeResult
, which holds the optimal value of lmbda in an attribute x.See the example below or the documentation of
scipy.optimize.minimize_scalar
for more information.- ymaxfloat, optional
The unconstrained optimal transform parameter may cause Box-Cox transformed data to have extreme magnitude or even overflow. This parameter constrains MLE optimization such that the magnitude of the transformed x does not exceed ymax. The default is the maximum value of the input dtype. If set to infinity,
boxcox_normmax
returns the unconstrained optimal lambda. Ignored whenmethod='pearsonr'
.
- Returns:
- maxlogfloat or ndarray
The optimal transform parameter found. An array instead of a scalar for
method='all'
.
Examples
>>> import numpy as np >>> from scipy import stats >>> import matplotlib.pyplot as plt
We can generate some data and determine the optimal
lmbda
in various ways:>>> rng = np.random.default_rng() >>> x = stats.loggamma.rvs(5, size=30, random_state=rng) + 5 >>> y, lmax_mle = stats.boxcox(x) >>> lmax_pearsonr = stats.boxcox_normmax(x)
>>> lmax_mle 2.217563431465757 >>> lmax_pearsonr 2.238318660200961 >>> stats.boxcox_normmax(x, method='all') array([2.23831866, 2.21756343])
>>> 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='--')
>>> plt.show()
Alternatively, we can define our own optimizer function. Suppose we are only interested in values of lmbda on the interval [6, 7], we want to use
scipy.optimize.minimize_scalar
withmethod='bounded'
, and we want to use tighter tolerances when optimizing the log-likelihood function. To do this, we define a function that accepts positional argument fun and usesscipy.optimize.minimize_scalar
to minimize fun subject to the provided bounds and tolerances:>>> from scipy import optimize >>> options = {'xatol': 1e-12} # absolute tolerance on `x` >>> def optimizer(fun): ... return optimize.minimize_scalar(fun, bounds=(6, 7), ... method="bounded", options=options) >>> stats.boxcox_normmax(x, optimizer=optimizer) 6.000...