bundles / scipy 1.18.0 / scipy / stats / _morestats / boxcox_normmax

function

`scipy.stats._morestats:boxcox_normmax`

source: /scipy/stats/_morestats.py:1263

Signature

def boxcox_normmax(x, brack = None, method = pearsonr, optimizer = None, *, ymax = BIG_FLOAT, nan_policy = propagate)

Summary

Compute optimal Box-Cox transform parameter for input data.

Parameters

x : array_like

Input array. All entries must be positive, finite, real numbers.

brack : 2-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.

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.
'mle': Maximizes the log-likelihood boxcox_llf. This is the method used in boxcox.
'all': Use all optimization methods available, and return all results. Useful to compare different methods.

optimizer : callable, optional

optimizer is a callable that accepts one argument:

fun: 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.

ymax : float, 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 when method='pearsonr'.

nan_policy : {'propagate', 'omit', 'raise'}

Defines how to handle input NaNs.

propagate: if a NaN is present in the input, the output will be NaN.
omit: NaNs will be omitted when performing the calculation.
raise: if a NaN is present, a ValueError will be raised.

Returns

maxlog : float 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
lmax_pearsonr
stats.boxcox_normmax(x, method='all')

✗

array([4.61002, 4.33238])

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='--')

✗

<matplotlib.lines.Line2D object at 0x7fa8fe6b1160>

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` with ``method='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 uses `scipy.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)

✗

np.float64(6.000000116308384)

Aliases

scipy.stats.boxcox_normmax