scipy.stats.boxcox#
- scipy.stats.boxcox(x, lmbda=None, alpha=None, optimizer=None)[source]#
Return a dataset transformed by a Box-Cox power transformation.
- Parameters:
- xndarray
Input array to be transformed.
If lmbda is not None, this is an alias of
scipy.special.boxcox
. Returns nan ifx < 0
; returns -inf ifx == 0 and lmbda < 0
.If lmbda is None, array must be positive, 1-dimensional, and non-constant.
- lmbdascalar, optional
If lmbda is None (default), find the value of lmbda that maximizes the log-likelihood function and return it as the second output argument.
If lmbda is not None, do the transformation for that value.
- alphafloat, optional
If lmbda is None and
alpha
is not None (default), return the100 * (1-alpha)%
confidence interval for lmbda as the third output argument. Must be between 0.0 and 1.0.If lmbda is not None,
alpha
is ignored.- optimizercallable, optional
If lmbda is None, optimizer is the scalar optimizer used to find the value of lmbda that minimizes the negative log-likelihood function. optimizer is a callable that accepts one argument:
- funcallable
The objective function, which evaluates the negative log-likelihood function at a provided value of lmbda
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 in
boxcox_normmax
or the documentation ofscipy.optimize.minimize_scalar
for more information.If lmbda is not None, optimizer is ignored.
- Returns:
- boxcoxndarray
Box-Cox power transformed array.
- maxlogfloat, optional
If the lmbda parameter is None, the second returned argument is the lmbda that maximizes the log-likelihood function.
- (min_ci, max_ci)tuple of float, optional
If lmbda parameter is None and
alpha
is not None, this returned tuple of floats represents the minimum and maximum confidence limits givenalpha
.
See also
Notes
The Box-Cox transform is given by:
y = (x**lmbda - 1) / lmbda, for lmbda != 0 log(x), for lmbda = 0
boxcox
requires the input data to be positive. Sometimes a Box-Cox transformation provides a shift parameter to achieve this;boxcox
does not. Such a shift parameter is equivalent to adding a positive constant to x before callingboxcox
.The confidence limits returned when
alpha
is provided give the interval where:\[llf(\hat{\lambda}) - llf(\lambda) < \frac{1}{2}\chi^2(1 - \alpha, 1),\]with
llf
the log-likelihood function and \(\chi^2\) the chi-squared function.References
G.E.P. Box and D.R. Cox, “An Analysis of Transformations”, Journal of the Royal Statistical Society B, 26, 211-252 (1964).
Examples
>>> from scipy import stats >>> import matplotlib.pyplot as plt
We generate some random variates from a non-normal distribution and make a probability plot for it, to show it is non-normal in the tails:
>>> fig = plt.figure() >>> ax1 = fig.add_subplot(211) >>> x = stats.loggamma.rvs(5, size=500) + 5 >>> prob = stats.probplot(x, dist=stats.norm, plot=ax1) >>> ax1.set_xlabel('') >>> ax1.set_title('Probplot against normal distribution')
We now use
boxcox
to transform the data so it’s closest to normal:>>> ax2 = fig.add_subplot(212) >>> xt, _ = stats.boxcox(x) >>> prob = stats.probplot(xt, dist=stats.norm, plot=ax2) >>> ax2.set_title('Probplot after Box-Cox transformation')
>>> plt.show()