API documentation¶
Module mixedvine¶
This module implements a copula vine model with mixed marginals.
Classes¶
- MixedVine
Copula vine model with mixed marginals.
- class mixedvines.mixedvine.MixedVine(dim)¶
Represents a copula vine model with mixed marginals.
- Parameters:
- dimint
The number of marginals of the vine model. Must be greater than 1.
- Raises:
- ValueError
If the number of marginals dim is not greater than 1.
- Attributes:
- root_VineLayer
The root layer of the vine tree.
Methods
entropy
([alpha, sem_tol, mc_size, random_state])Estimates the entropy of the mixed vine.
fit
(samples, is_continuous[, trunc_level, ...])Fits the mixed vine to the given samples.
Determines which marginals are continuous.
logpdf
(samples)Calculates the log of the probability density function.
pdf
(samples)Calculates the probability density function.
rvs
([size, random_state])Generates random variates from the mixed vine.
set_copula
(layer_index, copula_index, copula)Sets a pair-copula.
set_marginal
(marginal_index, rv_mixed)Sets a marginal distribution.
- entropy(alpha=0.05, sem_tol=0.001, mc_size=1000, random_state=None)¶
Estimates the entropy of the mixed vine.
- Parameters:
- alphafloat, optional
Significance level of the entropy estimate. (Default: 0.05)
- sem_tolfloat, optional
Maximum standard error as a stopping criterion. (Default: 1e-3)
- mc_sizeint, optional
Number of samples that are drawn in each iteration of the Monte Carlo estimation. (Default: 1000)
- random_state{None, int, numpy.random.Generator,
numpy.random.RandomState}, optional
The random state to use for random variate generation. None corresponds to the RandomState singleton. For an int, a new RandomState is genered and seeded. For a RandomState or Generator, the object is used. (Default: None)
- Returns:
- entfloat
Estimate of the mixed vine entropy in bits.
- semfloat
Standard error of the mixed vine entropy estimate in bits.
- static fit(samples, is_continuous, trunc_level=None, do_refine=False, keep_order=False)¶
Fits the mixed vine to the given samples.
- Parameters:
- samplesarray_like
n-by-d matrix of samples where n is the number of samples and d is the number of marginals.
- is_continuousarray_like
List of boolean values of length d, where d is the number of marginals and element i is True if marginal i is continuous.
- trunc_levelint, optional
Layer level to truncate the vine at. Copulas in layers beyond are just independence copulas. If the level is None, then the vine is not truncated. (Default: None)
- do_refineboolean, optional
If True, then all pair-copula parameters are optimized jointly at the end. (Default: False)
- keep_orderboolean, optional
If False, then a heuristic is used to select the vine structure. (Default: False)
- Returns:
- vineMixedVine
The mixed vine with parameters fitted to samples.
- is_continuous()¶
Determines which marginals are continuous.
- Returns:
- array_like
List of boolean values of length d, where d is the number of marginals and element i is True if marginal i is continuous.
- logpdf(samples)¶
Calculates the log of the probability density function.
- Parameters:
- samplesarray_like
n-by-d matrix of samples where n is the number of samples and d is the number of marginals.
- Returns:
- ndarray
Log of the probability density function evaluated at samples.
- pdf(samples)¶
Calculates the probability density function.
- Parameters:
- samplesarray_like
n-by-d matrix of samples where n is the number of samples and d is the number of marginals.
- Returns:
- ndarray
Probability density function evaluated at samples.
- rvs(size=1, random_state=None)¶
Generates random variates from the mixed vine.
- Parameters:
- sizeint, optional
The number of samples to generate. (Default: 1)
- random_state{None, int, numpy.random.Generator,
numpy.random.RandomState}, optional
The random state to use for random variate generation. None corresponds to the RandomState singleton. For an int, a new RandomState is generated and seeded. For a RandomState or Generator, the object is used. (Default: None)
- Returns:
- array_like
n-by-d matrix of samples where n is the number of samples and d is the number of marginals.
- set_copula(layer_index, copula_index, copula)¶
Sets a pair-copula.
Sets a particular pair-copula in the mixed vine tree for manual construction of a mixed vine model.
- Parameters:
- layer_indexint
The index of the vine layer.
- copula_indexint
The index of the copula in its layer.
- copulaCopula
The copula to be inserted.
- Raises:
- IndexError
If the argument layer_index is out of range.
- set_marginal(marginal_index, rv_mixed)¶
Sets a marginal distribution.
Sets a particular marginal distribution in the mixed vine tree for manual construction of a mixed vine model.
- Parameters:
- marginal_indexint
The index of the marginal in the marginal layer.
- rv_mixedscipy.stats.distributions.rv_frozen
The marginal distribution to be inserted.
Module marginal¶
This module implements univariate marginal distributions.
Classes¶
- Marginal
Discrete or continuous marginal distribution.
- class mixedvines.marginal.Marginal(rv_mixed)¶
Represents a continuous or discrete marginal distribution.
- Parameters:
- rv_mixedscipy.stats.distributions.rv_frozen
The distribution object, either of a continuous or of a discrete univariate distribution.
- Attributes:
- rv_mixedscipy.stats.distributions.rv_frozen
The distribution object.
- is_continuousboolean
True if the distribution is continuous.
Methods
cdf
(samples)Calculates the cumulative distribution function.
fit
(samples, is_continuous)Fits a distribution to the given samples.
logcdf
(samples)Calculates the log of the cumulative distribution function.
logpdf
(samples)Calculates the log of the probability density function.
pdf
(samples)Calculates the probability density function.
ppf
(samples)Calculates the inverse of the cumulative distribution function.
rvs
([size, random_state])Generates random variates from the distribution.
- cdf(samples)¶
Calculates the cumulative distribution function.
- Parameters:
- samplesarray_like
Array of samples.
- Returns:
- ndarray
Cumulative distribution function evaluated at samples.
- static fit(samples, is_continuous)¶
Fits a distribution to the given samples.
- Parameters:
- samplesarray_like
Array of samples.
- is_continuousboolean
If True then a continuous distribution is fitted. Otherwise, a discrete distribution is fitted.
- Returns:
- best_marginalMarginal
The distribution fitted to samples.
- logcdf(samples)¶
Calculates the log of the cumulative distribution function.
- Parameters:
- samplesarray_like
Array of samples.
- Returns:
- ndarray
Log of the cumulative distribution function evaluated at samples.
- logpdf(samples)¶
Calculates the log of the probability density function.
- Parameters:
- samplesarray_like
Array of samples.
- Returns:
- ndarray
Log of the probability density function evaluated at samples.
- pdf(samples)¶
Calculates the probability density function.
- Parameters:
- samplesarray_like
Array of samples.
- Returns:
- ndarray
Probability density function evaluated at samples.
- ppf(samples)¶
Calculates the inverse of the cumulative distribution function.
- Parameters:
- samplesarray_like
Array of samples.
- Returns:
- ndarray
Inverse of the cumulative distribution function evaluated at samples.
- rvs(size=1, random_state=None)¶
Generates random variates from the distribution.
- Parameters:
- sizeint, optional
The number of samples to generate. (Default: 1)
- random_state{None, int, numpy.random.Generator,
numpy.random.RandomState}, optional
The random state to use for random variate generation. None corresponds to the RandomState singleton. For an int, a new RandomState is generated and seeded. For a RandomState or Generator, the object is used. (Default: None)
- Returns:
- array_like
Array of samples.
Module copula¶
This module implements bivariate copula distributions.
Classes¶
- Copula
Abstract class representing a copula.
- IndependenceCopula
Independence copula.
- GaussianCopula
Copula from the Gaussian family.
- ClaytonCopula
Copula from the Clayton family.
- FrankCopula
Copula from the Frank family.
- class mixedvines.copula.ClaytonCopula(theta=None, rotation=None)¶
Bases:
Copula
This class represents a copula from the Clayton family.
Methods
ccdf
(samples[, axis])Calculates the conditional cumulative distribution function.
cdf
(samples)Calculates the cumulative distribution function.
estimate_theta
(samples)Estimates the theta parameters from the given samples.
fit
(samples)Fits the parameters of the copula to the given samples.
logcdf
(samples)Calculates the log of the cumulative distribution function.
logpdf
(samples)Calculates the log of the probability density function.
pdf
(samples)Calculates the probability density function.
ppcf
(samples[, axis])Calculates the inverse of the conditional CDF.
rvs
([size, random_state])Generates random variates from the copula.
Bounds for theta parameters.
- ccdf(samples, axis=1)¶
Calculates the conditional cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- axisint, optional
The axis to condition the cumulative distribution function on. (Default: 1)
- Returns:
- ndarray
Conditional cumulative distribution function evaluated at samples.
- cdf(samples)¶
Calculates the cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- ndarray
Cumulative distribution function evaluated at samples.
- estimate_theta(samples)¶
Estimates the theta parameters from the given samples.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- classmethod fit(samples)¶
Fits the parameters of the copula to the given samples.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- copulaCopula
The copula fitted to samples.
- logcdf(samples)¶
Calculates the log of the cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- valsndarray
Log of the cumulative distribution function evaluated at samples.
- logpdf(samples)¶
Calculates the log of the probability density function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- valsndarray
Log of the probability density function evaluated at samples.
- pdf(samples)¶
Calculates the probability density function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- ndarray
Probability density function evaluated at samples.
- ppcf(samples, axis=1)¶
Calculates the inverse of the conditional CDF.
Calculates the inverse of the copula conditional cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- axisint, optional
The axis to condition the cumulative distribution function on. (Default: 1)
- Returns:
- ndarray
Inverse of the conditional cumulative distribution function evaluated at samples.
- rvs(size=1, random_state=None)¶
Generates random variates from the copula.
- Parameters:
- sizeint, optional
The number of samples to generate. (Default: 1)
- random_state{None, int, numpy.random.Generator,
numpy.random.RandomState}, optional
The random state to use for random variate generation. None corresponds to the RandomState singleton. For an int, a new RandomState is generated and seeded. For a RandomState or Generator, the object is used. (Default: None)
- Returns:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- static theta_bounds()¶
Bounds for theta parameters.
- Returns:
- array_like
List of 2-tuples where the first tuple element represents the lower bound and the second element represents the upper bound.
- class mixedvines.copula.Copula(theta=None, rotation=None)¶
Bases:
ABC
This abstract class represents a copula.
- Parameters:
- thetaarray_like or float, optional
Parameter or parameter array of the copula. The number of elements depends on the copula family. (Default: None)
- rotationstring, optional
Clockwise rotation of the copula. Can be one of the elements of Copula.rotation_options or None. (Default: None)
- Attributes:
- thetaarray_like or float
Parameter or parameter array of the copula.
- rotationstring
Clockwise rotation of the copula.
Methods
ccdf
(samples[, axis])Calculates the conditional cumulative distribution function.
cdf
(samples)Calculates the cumulative distribution function.
estimate_theta
(samples)Estimates the theta parameters from the given samples.
fit
(samples)Fits the parameters of the copula to the given samples.
logcdf
(samples)Calculates the log of the cumulative distribution function.
logpdf
(samples)Calculates the log of the probability density function.
pdf
(samples)Calculates the probability density function.
ppcf
(samples[, axis])Calculates the inverse of the conditional CDF.
rvs
([size, random_state])Generates random variates from the copula.
Bounds for theta parameters.
- ccdf(samples, axis=1)¶
Calculates the conditional cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- axisint, optional
The axis to condition the cumulative distribution function on. (Default: 1)
- Returns:
- ndarray
Conditional cumulative distribution function evaluated at samples.
- cdf(samples)¶
Calculates the cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- ndarray
Cumulative distribution function evaluated at samples.
- estimate_theta(samples)¶
Estimates the theta parameters from the given samples.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- classmethod fit(samples)¶
Fits the parameters of the copula to the given samples.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- copulaCopula
The copula fitted to samples.
- logcdf(samples)¶
Calculates the log of the cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- valsndarray
Log of the cumulative distribution function evaluated at samples.
- logpdf(samples)¶
Calculates the log of the probability density function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- valsndarray
Log of the probability density function evaluated at samples.
- pdf(samples)¶
Calculates the probability density function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- ndarray
Probability density function evaluated at samples.
- ppcf(samples, axis=1)¶
Calculates the inverse of the conditional CDF.
Calculates the inverse of the copula conditional cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- axisint, optional
The axis to condition the cumulative distribution function on. (Default: 1)
- Returns:
- ndarray
Inverse of the conditional cumulative distribution function evaluated at samples.
- rvs(size=1, random_state=None)¶
Generates random variates from the copula.
- Parameters:
- sizeint, optional
The number of samples to generate. (Default: 1)
- random_state{None, int, numpy.random.Generator,
numpy.random.RandomState}, optional
The random state to use for random variate generation. None corresponds to the RandomState singleton. For an int, a new RandomState is generated and seeded. For a RandomState or Generator, the object is used. (Default: None)
- Returns:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- abstract static theta_bounds()¶
Bounds for theta parameters.
- Returns:
- array_like
List of 2-tuples where the first tuple element represents the lower bound and the second element represents the upper bound.
- class mixedvines.copula.FrankCopula(theta=None, rotation=None)¶
Bases:
Copula
This class represents a copula from the Frank family.
Methods
ccdf
(samples[, axis])Calculates the conditional cumulative distribution function.
cdf
(samples)Calculates the cumulative distribution function.
estimate_theta
(samples)Estimates the theta parameters from the given samples.
fit
(samples)Fits the parameters of the copula to the given samples.
logcdf
(samples)Calculates the log of the cumulative distribution function.
logpdf
(samples)Calculates the log of the probability density function.
pdf
(samples)Calculates the probability density function.
ppcf
(samples[, axis])Calculates the inverse of the conditional CDF.
rvs
([size, random_state])Generates random variates from the copula.
Bounds for theta parameters.
- ccdf(samples, axis=1)¶
Calculates the conditional cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- axisint, optional
The axis to condition the cumulative distribution function on. (Default: 1)
- Returns:
- ndarray
Conditional cumulative distribution function evaluated at samples.
- cdf(samples)¶
Calculates the cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- ndarray
Cumulative distribution function evaluated at samples.
- estimate_theta(samples)¶
Estimates the theta parameters from the given samples.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- classmethod fit(samples)¶
Fits the parameters of the copula to the given samples.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- copulaCopula
The copula fitted to samples.
- logcdf(samples)¶
Calculates the log of the cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- valsndarray
Log of the cumulative distribution function evaluated at samples.
- logpdf(samples)¶
Calculates the log of the probability density function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- valsndarray
Log of the probability density function evaluated at samples.
- pdf(samples)¶
Calculates the probability density function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- ndarray
Probability density function evaluated at samples.
- ppcf(samples, axis=1)¶
Calculates the inverse of the conditional CDF.
Calculates the inverse of the copula conditional cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- axisint, optional
The axis to condition the cumulative distribution function on. (Default: 1)
- Returns:
- ndarray
Inverse of the conditional cumulative distribution function evaluated at samples.
- rvs(size=1, random_state=None)¶
Generates random variates from the copula.
- Parameters:
- sizeint, optional
The number of samples to generate. (Default: 1)
- random_state{None, int, numpy.random.Generator,
numpy.random.RandomState}, optional
The random state to use for random variate generation. None corresponds to the RandomState singleton. For an int, a new RandomState is generated and seeded. For a RandomState or Generator, the object is used. (Default: None)
- Returns:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- static theta_bounds()¶
Bounds for theta parameters.
- Returns:
- array_like
List of 2-tuples where the first tuple element represents the lower bound and the second element represents the upper bound.
- class mixedvines.copula.GaussianCopula(theta=None, rotation=None)¶
Bases:
Copula
This class represents a copula from the Gaussian family.
Methods
ccdf
(samples[, axis])Calculates the conditional cumulative distribution function.
cdf
(samples)Calculates the cumulative distribution function.
estimate_theta
(samples)Estimates the theta parameters from the given samples.
fit
(samples)Fits the parameters of the copula to the given samples.
logcdf
(samples)Calculates the log of the cumulative distribution function.
logpdf
(samples)Calculates the log of the probability density function.
pdf
(samples)Calculates the probability density function.
ppcf
(samples[, axis])Calculates the inverse of the conditional CDF.
rvs
([size, random_state])Generates random variates from the copula.
Bounds for theta parameters.
- ccdf(samples, axis=1)¶
Calculates the conditional cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- axisint, optional
The axis to condition the cumulative distribution function on. (Default: 1)
- Returns:
- ndarray
Conditional cumulative distribution function evaluated at samples.
- cdf(samples)¶
Calculates the cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- ndarray
Cumulative distribution function evaluated at samples.
- estimate_theta(samples)¶
Estimates the theta parameters from the given samples.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- classmethod fit(samples)¶
Fits the parameters of the copula to the given samples.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- copulaCopula
The copula fitted to samples.
- logcdf(samples)¶
Calculates the log of the cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- valsndarray
Log of the cumulative distribution function evaluated at samples.
- logpdf(samples)¶
Calculates the log of the probability density function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- valsndarray
Log of the probability density function evaluated at samples.
- pdf(samples)¶
Calculates the probability density function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- ndarray
Probability density function evaluated at samples.
- ppcf(samples, axis=1)¶
Calculates the inverse of the conditional CDF.
Calculates the inverse of the copula conditional cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- axisint, optional
The axis to condition the cumulative distribution function on. (Default: 1)
- Returns:
- ndarray
Inverse of the conditional cumulative distribution function evaluated at samples.
- rvs(size=1, random_state=None)¶
Generates random variates from the copula.
- Parameters:
- sizeint, optional
The number of samples to generate. (Default: 1)
- random_state{None, int, numpy.random.Generator,
numpy.random.RandomState}, optional
The random state to use for random variate generation. None corresponds to the RandomState singleton. For an int, a new RandomState is generated and seeded. For a RandomState or Generator, the object is used. (Default: None)
- Returns:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- static theta_bounds()¶
Bounds for theta parameters.
- Returns:
- array_like
List of 2-tuples where the first tuple element represents the lower bound and the second element represents the upper bound.
- class mixedvines.copula.IndependenceCopula(theta=None, rotation=None)¶
Bases:
Copula
This class represents the independence copula.
Methods
ccdf
(samples[, axis])Calculates the conditional cumulative distribution function.
cdf
(samples)Calculates the cumulative distribution function.
estimate_theta
(samples)Estimates the theta parameters from the given samples.
fit
(samples)Fits the parameters of the copula to the given samples.
logcdf
(samples)Calculates the log of the cumulative distribution function.
logpdf
(samples)Calculates the log of the probability density function.
pdf
(samples)Calculates the probability density function.
ppcf
(samples[, axis])Calculates the inverse of the conditional CDF.
rvs
([size, random_state])Generates random variates from the copula.
Bounds for theta parameters.
- ccdf(samples, axis=1)¶
Calculates the conditional cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- axisint, optional
The axis to condition the cumulative distribution function on. (Default: 1)
- Returns:
- ndarray
Conditional cumulative distribution function evaluated at samples.
- cdf(samples)¶
Calculates the cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- ndarray
Cumulative distribution function evaluated at samples.
- estimate_theta(samples)¶
Estimates the theta parameters from the given samples.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- classmethod fit(samples)¶
Fits the parameters of the copula to the given samples.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- copulaCopula
The copula fitted to samples.
- logcdf(samples)¶
Calculates the log of the cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- valsndarray
Log of the cumulative distribution function evaluated at samples.
- logpdf(samples)¶
Calculates the log of the probability density function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- valsndarray
Log of the probability density function evaluated at samples.
- pdf(samples)¶
Calculates the probability density function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- Returns:
- ndarray
Probability density function evaluated at samples.
- ppcf(samples, axis=1)¶
Calculates the inverse of the conditional CDF.
Calculates the inverse of the copula conditional cumulative distribution function.
- Parameters:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- axisint, optional
The axis to condition the cumulative distribution function on. (Default: 1)
- Returns:
- ndarray
Inverse of the conditional cumulative distribution function evaluated at samples.
- rvs(size=1, random_state=None)¶
Generates random variates from the copula.
- Parameters:
- sizeint, optional
The number of samples to generate. (Default: 1)
- random_state{None, int, numpy.random.Generator,
numpy.random.RandomState}, optional
The random state to use for random variate generation. None corresponds to the RandomState singleton. For an int, a new RandomState is generated and seeded. For a RandomState or Generator, the object is used. (Default: None)
- Returns:
- samplesarray_like
n-by-2 matrix of samples where n is the number of samples.
- static theta_bounds()¶
Bounds for theta parameters.
- Returns:
- array_like
List of 2-tuples where the first tuple element represents the lower bound and the second element represents the upper bound.