skpro.distributions.QPD_U

class skpro.distributions.QPD_U(alpha: float, qv_low: float, qv_median: float, qv_high: float, version: str | None = 'normal', dist_shape: float | None = 0.0, index=None, columns=None)

Johnson Quantile-Parameterized Distributions with unbounded mode.

see https://repositories.lib.utexas.edu/bitstream/handle/2152

/63037/HADLOCK-DISSERTATION-2017.pdf

(Due to the Python keyword, the parameter lambda from this reference is named kappa below). A distribution is parameterized by a symmetric-percentile triplet (SPT).

Parameters:

alphafloat

lower quantile of SPT (upper is 1 - alpha)

qv_lowfloat or array_like[float]

quantile function value of alpha

qv_medianfloat or array_like[float]

quantile function value of quantile 0.5

qv_highfloat or array_like[float]

quantile function value of quantile 1 - alpha

version: str, optional, default=”normal”

options are normal (default) or logistic

dist_shape: float, optional, default=0.0

parameter modifying the logistic base distribution via sinh/arcsinh-scaling (only active in sinhlogistic version)

Attributes:

at

Integer location indexer, for single index.

iat

Integer location indexer, for single index.

iloc

Integer location indexer, for groups of indices.

loc

Location indexer, for groups of indices.

name

Return the name of the object or estimator.

ndim

Number of dimensions of self.

shape

Shape of self, a pair (2-tuple).

Methods

cdf(x)	Cumulative distribution function.
clone()	Obtain a clone of the object with same hyper-parameters.
clone_tags(estimator[, tag_names])	Clone tags from another estimator as dynamic override.
create_test_instance([parameter_set])	Construct Estimator instance if possible.
create_test_instances_and_names([parameter_set])	Create list of all test instances and a list of names for them.
energy([x])	Energy of self, w.r.t.
get_class_tag(tag_name[, tag_value_default])	Get a class tag's value.
get_class_tags()	Get class tags from the class and all its parent classes.
get_config()	Get config flags for self.
get_param_defaults()	Get object's parameter defaults.
get_param_names()	Get object's parameter names.
get_params([deep])	Get a dict of parameters values for this object.
get_params_df()	Return distribution parameters in a dict of DataFrame.
get_tag(tag_name[, tag_value_default, ...])	Get tag value from estimator class and dynamic tag overrides.
get_tags()	Get tags from estimator class and dynamic tag overrides.
get_test_params([parameter_set])	Return testing parameter settings for the estimator.
haz(x)	Hazard function.
is_composite()	Check if the object is composed of other BaseObjects.
log_pdf(x)	Logarithmic probability density function.
log_pmf(x)	Logarithmic probability mass function.
mean([lower, upper])	Return expected value of the distribution.
pdf(x)	Probability density function.
pdfnorm([a])	a-norm of pdf, defaults to 2-norm.
plot([fun, ax])	Plot the distribution.
pmf(x)	Probability mass function.
ppf(p)	Quantile function = percent point function = inverse cdf.
quantile(alpha)	Return entry-wise quantiles, in Proba/pred_quantiles mtype format.
reset()	Reset the object to a clean post-init state.
sample([n_samples])	Sample from the distribution.
set_config(**config_dict)	Set config flags to given values.
set_params(**params)	Set the parameters of this object.
set_random_state([random_state, deep, ...])	Set random_state pseudo-random seed parameters for self.
set_tags(**tag_dict)	Set dynamic tags to given values.
surv(x)	Survival function.
to_df()	Return distribution parameters as a single DataFrame.
to_str()	Return string representation of self.
var([lower, upper])	Return element/entry-wise variance of the distribution.

property at

Integer location indexer, for single index.

Use my_distribution.at[index] for pandas-like row/column subsetting of BaseDistribution descendants.

index can be any pandas at compatible index subsetter.

my_distribution.at[index] or my_distribution.at[row_index, col_index] subset my_distribution to the row selected by row_index, col by col_index, to exactly the same col/rows as pandas at would subset rows in my_distribution.index and columns in my_distribution.columns.

clone()

Obtain a clone of the object with same hyper-parameters.

A clone is a different object without shared references, in post-init state. This function is equivalent to returning sklearn.clone of self.

Raises:

RuntimeError if the clone is non-conforming, due to faulty __init__.

Notes

If successful, equal in value to type(self)(**self.get_params(deep=False)).

clone_tags(estimator, tag_names=None)

Clone tags from another estimator as dynamic override.

Parameters:

estimatorestimator inheriting from :class:BaseEstimator

tag_namesstr or list of str, default = None

Names of tags to clone. If None then all tags in estimator are used as tag_names.

Returns:

Self

Reference to self.

Notes

Changes object state by setting tag values in tag_set from estimator as dynamic tags in self.

classmethod create_test_instance(parameter_set='default')

Construct Estimator instance if possible.

Parameters:

parameter_setstr, default=”default”

Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

Returns:

instanceinstance of the class with default parameters

Notes

get_test_params can return dict or list of dict. This function takes first or single dict that get_test_params returns, and constructs the object with that.

classmethod create_test_instances_and_names(parameter_set='default')

Create list of all test instances and a list of names for them.

Parameters:

parameter_setstr, default=”default”

Name of the set of test parameters to return, for use in tests. If no special parameters are defined for a value, will return “default” set.

Returns:

objslist of instances of cls

i-th instance is cls(**cls.get_test_params()[i])

nameslist of str, same length as objs

i-th element is name of i-th instance of obj in tests convention is {cls.__name__}-{i} if more than one instance otherwise {cls.__name__}

energy(x=None)

Energy of self, w.r.t. self or a constant frame x.

Let \(X, Y\) be i.i.d. random variables with the distribution of self.

If x is None, returns \(\mathbb{E}[|X-Y|]\) (per row), “self-energy”. If x is passed, returns \(\mathbb{E}[|X-x|]\) (per row), “energy wrt x”.

The CRPS is related to energy: it holds that \(\mbox{CRPS}(\mbox{self}, y)\) = self.energy(y) - 0.5 * self.energy().

Parameters:

xNone or pd.DataFrame, optional, default=None

if pd.DataFrame, must have same rows and columns as self

Returns:

pd.DataFrame with same rows as self, single column "energy"

each row contains one float, self-energy/energy as described above.

classmethod get_class_tag(tag_name, tag_value_default=None)

Get a class tag’s value.

Does not return information from dynamic tags (set via set_tags or clone_tags) that are defined on instances.

Parameters:

tag_namestr

Name of tag value.

tag_value_defaultany

Default/fallback value if tag is not found.

Returns:

tag_value

Value of the tag_name tag in self. If not found, returns tag_value_default.

classmethod get_class_tags()

Get class tags from the class and all its parent classes.

Retrieves tag: value pairs from _tags class attribute. Does not return information from dynamic tags (set via set_tags or clone_tags) that are defined on instances.

Returns:

collected_tagsdict

Dictionary of class tag name: tag value pairs. Collected from _tags class attribute via nested inheritance.

get_config()

Get config flags for self.

Returns:

config_dictdict

Dictionary of config name : config value pairs. Collected from _config class attribute via nested inheritance and then any overrides and new tags from _onfig_dynamic object attribute.

classmethod get_param_defaults()

Get object’s parameter defaults.

Returns:

default_dict: dict[str, Any]

Keys are all parameters of cls that have a default defined in __init__ values are the defaults, as defined in __init__.

classmethod get_param_names()

Get object’s parameter names.

Returns:

param_names: list[str]

Alphabetically sorted list of parameter names of cls.

get_params(deep=True)

Get a dict of parameters values for this object.

Parameters:

deepbool, default=True

Whether to return parameters of components.

• If True, will return a dict of parameter name : value for this object, including parameters of components (= BaseObject-valued parameters).

• If False, will return a dict of parameter name : value for this object, but not include parameters of components.

Returns:

paramsdict with str-valued keys

Dictionary of parameters, paramname : paramvalue keys-value pairs include:

• always: all parameters of this object, as via get_param_names values are parameter value for that key, of this object values are always identical to values passed at construction

• if deep=True, also contains keys/value pairs of component parameters parameters of components are indexed as [componentname]__[paramname] all parameters of componentname appear as paramname with its value

• if deep=True, also contains arbitrary levels of component recursion, e.g., [componentname]__[componentcomponentname]__[paramname], etc

get_params_df()

Return distribution parameters in a dict of DataFrame.

Available only for simple parametric distributions, i.e., distributions with tag “distr:paramtype” having value “parametric”.

Returns:

dict of pd.DataFrame

Dictionary with all distribution parameters, as pd.DataFrame. Keys are the parameter names, values are the pd.DataFrame. Each DataFrame has the same index as self and columns as self. Entries are the values of the distribution parameters.

get_tag(tag_name, tag_value_default=None, raise_error=True)

Get tag value from estimator class and dynamic tag overrides.

Parameters:

tag_namestr

Name of tag to be retrieved

tag_value_defaultany type, optional; default=None

Default/fallback value if tag is not found

raise_errorbool

whether a ValueError is raised when the tag is not found

Returns:

tag_valueAny

Value of the tag_name tag in self. If not found, returns an error if raise_error is True, otherwise it returns tag_value_default.

Raises:

ValueError if raise_error is True i.e. if tag_name is not in

self.get_tags().keys()

get_tags()

Get tags from estimator class and dynamic tag overrides.

Returns:

collected_tagsdict

Dictionary of tag name : tag value pairs. Collected from _tags class attribute via nested inheritance and then any overrides and new tags from _tags_dynamic object attribute.

haz(x)

Hazard function.

Let \(X\) be a random variables with the distribution of self, taking values in (N, n) DataFrame-s Let \(x\in \mathbb{R}^{N\times n}\). By \(h_{X_{ij}}\), denote the marginal hazard of \(X\) at the \((i,j)\)-th entry, i.e., \(h_{X_{ij}}(t) = \frac{f_{X_{ij}}(t)}{S_{X_{ij}}(t)}\), where \(f_{X_{ij}}\) is the marginal pdf, and \(S_{X_{ij}}\) is the marginal survival function at the \((i,j)\)-th entry.

The output of this method, for input x representing \(x\), is a DataFrame with same columns and indices as self, and entries \(h_{X_{ij}}(x_{ij})\).

Parameters:

xpandas.DataFrame or 2D np.ndarray

representing \(x\), as above

Returns:

pd.DataFrame with same columns and index as self

containing \(h_{X_{ij}}(x_{ij})\), as above

property iat

Integer location indexer, for single index.

Use my_distribution.iat[index] for pandas-like row/column subsetting of BaseDistribution descendants.

index can be any pandas iat compatible index subsetter.

my_distribution.iat[index] or my_distribution.iat[row_index, col_index] subset my_distribution to the row selected by row_index, col by col_index, to exactly the same col/rows as pandas iat would subset rows in my_distribution.index and columns in my_distribution.columns.

property iloc

Integer location indexer, for groups of indices.

Use my_distribution.iloc[index] for pandas-like row/column subsetting of BaseDistribution descendants.

index can be any pandas iloc compatible index subsetter.

my_distribution.iloc[index] or my_distribution.iloc[row_index, col_index] subset my_distribution to rows selected by row_index, cols by col_index, to exactly the same cols/rows as pandas iloc would subset rows in my_distribution.index and columns in my_distribution.columns.

is_composite()

Check if the object is composed of other BaseObjects.

A composite object is an object which contains objects, as parameters. Called on an instance, since this may differ by instance.

Returns:

composite: bool

Whether an object has any parameters whose values are BaseObjects.

property loc

Location indexer, for groups of indices.

Use my_distribution.loc[index] for pandas-like row/column subsetting of BaseDistribution descendants.

index can be any pandas iloc compatible index subsetter.

my_distribution.loc[index] or my_distribution.loc[row_index, col_index] subset my_distribution to rows selected by row_index, cols by col_index, to exactly the same cols/rows as pandas loc would subset rows in my_distribution.index and columns in my_distribution.columns.

log_pdf(x)

Logarithmic probability density function.

Numerically more stable than calling pdf and then taking logartihms.

Let \(X\) be a random variables with the distribution of self, taking values in (N, n) DataFrame-s Let \(x\in \mathbb{R}^{N\times n}\). By \(p_{X_{ij}}\), denote the marginal pdf of \(X\) at the \((i,j)\)-th entry.

The output of this method, for input x representing \(x\), is a DataFrame with same columns and indices as self, and entries \(\log p_{X_{ij}}(x_{ij})\).

If self has a mixed or discrete distribution, this returns the weighted continuous part of self’s distribution instead of the pdf, i.e., the marginal pdf integrate to the weight of the continuous part.

Parameters:

xpandas.DataFrame or 2D np.ndarray

representing \(x\), as above

Returns:

pd.DataFrame with same columns and index as self

containing \(\log p_{X_{ij}}(x_{ij})\), as above

log_pmf(x)

Logarithmic probability mass function.

Numerically more stable than calling pmf and then taking logartihms.

Let \(X\) be a random variables with the distribution of self, taking values in (N, n) DataFrame-s Let \(x\in \mathbb{R}^{N\times n}\). By \(m_{X_{ij}}\), denote the marginal pdf of \(X\) at the \((i,j)\)-th entry, i.e., \(m_{X_{ij}}(x_{ij}) = \mathbb{P}(X_{ij} = x_{ij})\).

The output of this method, for input x representing \(x\), is a DataFrame with same columns and indices as self, and entries \(\log m_{X_{ij}}(x_{ij})\).

If self has a mixed or discrete distribution, this returns the weighted continuous part of self’s distribution instead of the pdf, i.e., the marginal pdf integrate to the weight of the continuous part.

Parameters:

xpandas.DataFrame or 2D np.ndarray

representing \(x\), as above

Returns:

pd.DataFrame with same columns and index as self

containing \(\log m_{X_{ij}}(x_{ij})\), as above

property name

Return the name of the object or estimator.

property ndim

Number of dimensions of self. 2 if array, 0 if scalar.

pdfnorm(a=2)

a-norm of pdf, defaults to 2-norm.

computes a-norm of the entry marginal pdf, i.e., \(\mathbb{E}[p_X(X)^{a-1}] = \int p(x)^a dx\), where \(X\) is a random variable distributed according to the entry marginal of self, and \(p_X\) is its pdf

Parameters:

a: int or float, optional, default=2

Returns:

pd.DataFrame with same rows and columns as self

each entry is \(\mathbb{E}[p_X(X)^{a-1}] = \int p(x)^a dx\), see above

plot(fun='pdf', ax=None, **kwargs)

Plot the distribution.

Different distribution defining functions can be selected for plotting via the fun parameter. The functions available are the same as the methods of the distribution class, e.g., "pdf", "cdf", "ppf".

For array distribution, the marginal distribution at each entry is plotted, as a separate subplot.

Parameters:

funstr, optional, default=”pdf”

the function to plot, one of “pdf”, “cdf”, “ppf”

axmatplotlib Axes object, optional

matplotlib Axes to plot in if not provided, defaults to current axes (plot.gca)

kwargskeyword arguments

passed to the plotting function

Returns:

figmatplotlib.Figure, only returned if self is array distribution

matplotlig Figure object for subplots

axmatplotlib.Axes

the axis or axes on which the plot is drawn

pmf(x)

Probability mass function.

Let \(X\) be a random variables with the distribution of self, taking values in (N, n) DataFrame-s Let \(x\in \mathbb{R}^{N\times n}\). By \(m_{X_{ij}}\), denote the marginal mass of \(X\) at the \((i,j)\)-th entry, i.e., \(m_{X_{ij}}(x_{ij}) = \mathbb{P}(X_{ij} = x_{ij})\).

The output of this method, for input x representing \(x\), is a DataFrame with same columns and indices as self, and entries \(m_{X_{ij}}(x_{ij})\).

If self has a mixed or discrete distribution, this returns the weighted continuous part of self’s distribution instead of the pdf, i.e., the marginal pdf integrate to the weight of the continuous part.

Parameters:

xpandas.DataFrame or 2D np.ndarray

representing \(x\), as above

Returns:

pd.DataFrame with same columns and index as self

containing \(p_{X_{ij}}(x_{ij})\), as above

quantile(alpha)

Return entry-wise quantiles, in Proba/pred_quantiles mtype format.

This method broadcasts as follows: for a scalar alpha, computes the alpha-quantile entry-wise, and returns as a pd.DataFrame with same index, and columns as in return. If alpha is iterable, multiple quantiles will be calculated, and the result will be concatenated column-wise (axis=1).

The ppf method also computes quantiles, but broadcasts differently, in numpy style closer to tensorflow. In contrast, this quantile method broadcasts as sktime forecaster predict_quantiles, i.e., columns first.

Parameters:

alphafloat or list of float of unique values

A probability or list of, at which quantiles are computed.

Returns:

quantilespd.DataFrame

Column has multi-index: first level is variable name from self.columns, second level being the values of alpha passed to the function. Row index is self.index. Entries in the i-th row, (j, p)-the column is the p-th quantile of the marginal of self at index (i, j).

reset()

Reset the object to a clean post-init state.

Using reset, runs __init__ with current values of hyper-parameters (result of get_params). This Removes any object attributes, except:

• hyper-parameters = arguments of __init__

• object attributes containing double-underscores, i.e., the string “__”

Class and object methods, and class attributes are also unaffected.

Returns:

self

Instance of class reset to a clean post-init state but retaining the current hyper-parameter values.

Notes

Equivalent to sklearn.clone but overwrites self. After self.reset() call, self is equal in value to type(self)(**self.get_params(deep=False))

sample(n_samples=None)

Sample from the distribution.

Parameters:

n_samplesint, optional, default = None

Returns:

if n_samples is None:

returns a sample that contains a single sample from self,

in pd.DataFrame mtype format convention, with index and columns as self

if n_samples is int:

returns a pd.DataFrame that contains n_samples i.i.d. samples from self,

in pd-multiindex mtype format convention, with same columns as self,

and MultiIndex that is product of RangeIndex(n_samples) and self.index

set_config(**config_dict)

Set config flags to given values.

Parameters:

config_dictdict

Dictionary of config name : config value pairs.

Returns:

selfreference to self.

Notes

Changes object state, copies configs in config_dict to self._config_dynamic.

set_params(**params)

Set the parameters of this object.

The method works on simple estimators as well as on composite objects. Parameter key strings <component>__<parameter> can be used for composites, i.e., objects that contain other objects, to access <parameter> in the component <component>. The string <parameter>, without <component>__, can also be used if this makes the reference unambiguous, e.g., there are no two parameters of components with the name <parameter>.

Parameters:

**paramsdict

BaseObject parameters, keys must be <component>__<parameter> strings. __ suffixes can alias full strings, if unique among get_params keys.

Returns:

selfreference to self (after parameters have been set)

set_random_state(random_state=None, deep=True, self_policy='copy')

Set random_state pseudo-random seed parameters for self.

Finds random_state named parameters via estimator.get_params, and sets them to integers derived from random_state via set_params. These integers are sampled from chain hashing via sample_dependent_seed, and guarantee pseudo-random independence of seeded random generators.

Applies to random_state parameters in estimator depending on self_policy, and remaining component estimators if and only if deep=True.

Note: calls set_params even if self does not have a random_state, or none of the components have a random_state parameter. Therefore, set_random_state will reset any scikit-base estimator, even those without a random_state parameter.

Parameters:

random_stateint, RandomState instance or None, default=None

Pseudo-random number generator to control the generation of the random integers. Pass int for reproducible output across multiple function calls.

deepbool, default=True

Whether to set the random state in sub-estimators. If False, will set only self’s random_state parameter, if exists. If True, will set random_state parameters in sub-estimators as well.

self_policystr, one of {“copy”, “keep”, “new”}, default=”copy”

• “copy” : estimator.random_state is set to input random_state

• “keep” : estimator.random_state is kept as is

• “new” : estimator.random_state is set to a new random state,

derived from input random_state, and in general different from it

Returns:

selfreference to self

set_tags(**tag_dict)

Set dynamic tags to given values.

Parameters:

**tag_dictdict

Dictionary of tag name: tag value pairs.

Returns:

Self

Reference to self.

Notes

Changes object state by setting tag values in tag_dict as dynamic tags in self.

property shape

Shape of self, a pair (2-tuple).

surv(x)

Survival function.

Let \(X\) be a random variables with the distribution of self, taking values in (N, n) DataFrame-s Let \(x\in \mathbb{R}^{N\times n}\). By \(S_{X_{ij}}\), denote the marginal survival of \(X\) at the \((i,j)\)-th entry, i.e., \(S_{X_{ij}}(t) = \mathbb{P}(X_{ij} \gneq t)\).

The output of this method, for input x representing \(x\), is a DataFrame with same columns and indices as self, and entries \(F_{X_{ij}}(x_{ij})\).

Parameters:

xpandas.DataFrame or 2D np.ndarray

representing \(x\), as above

Returns:

pd.DataFrame with same columns and index as self

containing \(S_{X_{ij}}(x_{ij})\), as above

to_df()

Return distribution parameters as a single DataFrame.

Available only for simple parametric distributions, i.e., distributions with tag “distr:paramtype” having value “parametric”.

Returns:

pd.DataFrame

DataFrame with all distribution parameters. column is a MultiIndex (paramname, varname). row index is the index of the distribution. Entries are the values of the distribution parameters.

to_str()

Return string representation of self.

mean(lower=0.0, upper=inf)

Return expected value of the distribution.

Returns:

pd.DataFrame with same rows, columns as self

expected value of distribution (entry-wise)

var(lower=0.0, upper=inf)

Return element/entry-wise variance of the distribution.

Returns:

pd.DataFrame with same rows, columns as self

variance of distribution (entry-wise)

pdf(x: DataFrame)

Probability density function.

this fucntion transform cdf to pdf because j-qpd’s pdf calculation is bit complex

ppf(p: DataFrame)

Quantile function = percent point function = inverse cdf.

cdf(x: DataFrame)

Cumulative distribution function.

classmethod get_test_params(parameter_set='default')

Return testing parameter settings for the estimator.