# gstools.normalizer.Manly

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

Bases: Normalizer

Manly (1971) 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 [Manly1976]:

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

References

Manly1976

B. F. J. Manly, “Exponential data transformations.”, Journal of the Royal Statistical Society D, 25.1, 37-42 (1976).

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 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
Returns

Optimal parameters 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 Manly-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 = (-inf, inf)

Valid range for input data.

Type

tuple