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# scipy.stats.boxcox_normmax

scipy.stats.boxcox_normmax(x, brack=None, method='pearsonr', optimizer=None, *, ymax=BIG_FLOAT)

  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:

      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.

    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'`.

  Returns:
    maxlog float or ndarray

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

  See also

  `boxcox`, `boxcox_llf`, `boxcox_normplot`, `scipy.optimize.minimize_scalar`

  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` 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)
      6.000...