gstools.normalizer.BoxCox¶

class gstools.normalizer.BoxCox(data=None, **parameter)[source]¶

Bases: gstools.normalizer.base.Normalizer

Box-Cox (1964) transformed fields.

Parameters

data (array_like, optional) – Input data to fit the transformation in order to gain normality. The default is None.
lmbda (float, optional) – Shape parameter. Default: 1

Notes

This transformation is given by [Box1964]:

$y=\begin{cases} \frac{x^{\lambda} - 1}{\lambda} & \lambda\neq 0 \\ \log(x) & \lambda = 0 \end{cases}$

References

Box1964: G.E.P. Box and D.R. Cox, “An Analysis of Transformations”, Journal of the Royal Statistical Society B, 26, 211-252, (1964)

Attributes

denormalize_range: tuple: Valid range for output data depending on lmbda.
name: str: The name of the normalizer class.

Methods

`denormalize`(data)	Transform to input distribution.
`derivative`(data)	Factor for normal PDF to gain target PDF.
`fit`(data[, skip])	Fitting the transformation to data by maximizing Log-Likelihood.
`kernel_loglikelihood`(data)	Kernel Log-Likelihood for given data with current parameters.
`likelihood`(data)	Likelihood for given data with current parameters.
`loglikelihood`(data)	Log-Likelihood for given data with current parameters.
`normalize`(data)	Transform to normal distribution.

denormalize(data)¶

Transform to input distribution.

Parameters: data (array_like) – Input data (normal distributed).
Returns: Denormalized data.
Return type: numpy.ndarray

derivative(data)¶

Factor for normal PDF to gain target PDF.

Parameters: data (array_like) – Input data (not normal distributed).
Returns: Derivative of the normalization transformation function.
Return type: numpy.ndarray

fit(data, skip=None, **kwargs)¶

Fitting the transformation to data by maximizing Log-Likelihood.

Parameters

data (array_like) – Input data to fit the transformation to in order to gain normality.
skip (list of str or None, optional) – Names of parameters to be skiped in fitting. The default is None.
**kwargs – Keyword arguments passed to scipy.optimize.minimize_scalar when only one parameter present or scipy.optimize.minimize.

Returns

Optimal paramters given by names.

Return type

dict

kernel_loglikelihood(data)¶

Kernel Log-Likelihood for given data with current parameters.

Parameters: data (array_like) – Input data to fit the transformation to in order to gain normality.
Returns: Kernel Log-Likelihood of the given data.
Return type: float

Notes

This loglikelihood function is neglecting additive constants, that are not needed for optimization.

likelihood(data)¶

Likelihood for given data with current parameters.

Parameters: data (array_like) – Input data to fit the transformation to in order to gain normality.
Returns: Likelihood of the given data.
Return type: float

loglikelihood(data)¶

Log-Likelihood for given data with current parameters.

Parameters: data (array_like) – Input data to fit the transformation to in order to gain normality.
Returns: Log-Likelihood of the given data.
Return type: float

normalize(data)¶

Transform to normal distribution.

Parameters: data (array_like) – Input data (not normal distributed).
Returns: Normalized data.
Return type: numpy.ndarray

default_parameter = {'lmbda': 1}¶

Default parameter of the BoxCox-Normalizer.

Type: dict

property denormalize_range¶

Valid range for output data depending on lmbda.

(-1/lmbda, inf) or (-inf, -1/lmbda)

Type: tuple

property name¶

The name of the normalizer class.

Type: str

normalize_range = (0.0, inf)¶

Valid range for input data.

Type: tuple