pyuncertainnumber.pba.pbox_free

Attributes

known_constraints

Functions

KS_bounds(...)	construct free pbox from sample data by Kolmogorov-Smirnoff confidence bounds
known_properties(...)	Construct a uncertain number given known statistical properties served as constraints.
min_max(...)	Equivalent to an interval object constructed as a nonparametric Pbox.
min_mean(...)	Nonparametric pbox construction based on constraint of minimum and mean
mean_std(...)	Nonparametric pbox construction based on constraint of mean and std
mean_var(...)	Nonparametric pbox construction based on constraint of mean and var
min_max_mean(...)	Generates a distribution-free p-box based upon the minimum, maximum and mean of the variable
pos_mean_std(→ pyuncertainnumber.pba.pbox_abc.Pbox)	Generates a positive distribution-free p-box based upon the mean and standard deviation of the variable
min_max_mode(...)	Nonparametric pbox construction based on constraint of mean and var
min_max_median(...)	Generates a distribution-free p-box based upon the minimum, maximum and median of the variable
min_max_mean_std(...)	Generates a distribution-free p-box based upon the minimum, maximum, mean and standard deviation of the variable
min_max_mean_var(...)	Generates a distribution-free p-box based upon the minimum, maximum, mean and standard deviation of the variable
from_percentiles(...)	yields a distribution-free p-box based on specified percentiles of the variable

Module Contents

pyuncertainnumber.pba.pbox_free.KS_bounds(s: numpy.typing.ArrayLike, alpha: float, display=True, output_type='bounds') → tuple[pyuncertainnumber.pba.ecdf.eCDF_bundle] | pyuncertainnumber.pba.pbox_abc.Pbox | pyuncertainnumber.UncertainNumber

construct free pbox from sample data by Kolmogorov-Smirnoff confidence bounds

Parameters:

• s (ArrayLike) – sample data, precise and imprecise

• dn (float) – KS critical value at a significance level and sample size N;

• output_type (str) – A choice between {‘bounds’, ‘pbox’, ‘un’}, default=’bounds’ which returns two eCDF bundles as bounds; ‘pbox’ to return a pbox object; ‘un’ to return an uncertain number object.

Returns:

a tuple of two CDF bounds, i.e. upper and lower (eCDF_bundle objects), or a Pbox object, or an UncertainNumber object the return type is controlled by the output_type argument.

Note

By default the function returns two eCDF bundles as the extreme bounds. With the upper and lower bounds, a free pbox can be constructed.

Example

>>> # both precise data (e.g. numpy array) and imprecise data (e.g. a vector of interval) are supported
>>> precise_data = np.random.normal(0, 1, 100)  # precise data case
>>> ub, lb = pba.KS_bounds(precise_data, alpha=0.025, display=True)

>>> # alternatively, an uncertain number or a p-box can be returned
>>> pba.KS_bounds(precise_data, alpha=0.025, display=False, output_type='pbox')  # return a pbox object
>>> pba.KS_bounds(precise_data, alpha=0.025, display=False, output_type='un')  # return an uncertain number object

>>> # imprecise data case
>>> impre_data = pba.I(lo = precise_data -0.5, hi = precise_data + 0.5)
>>> ub, lb = pba.KS_bounds(impre_data, alpha=0.025, display=True)

Kolmogorov-Smirnoff confidence bounds illustration with precise and imprecise data.

pyuncertainnumber.pba.pbox_free.known_properties(maximum=None, mean=None, median=None, minimum=None, mode=None, percentiles=None, std=None, var=None, family=None, **kwargs) → pyuncertainnumber.characterisation.uncertainNumber.UncertainNumber

Construct a uncertain number given known statistical properties served as constraints.

Parameters:

• maximum (number) – maximum value of the variable

• mean (number) – mean value of the variable

• median (number) – median value of the variable

• minimum (number) – minimum value of the variable

• mode (number) – mode value of the variable

• percentiles (dict) – dictionary of percentiles and their values, e.g. {0: 0, 0.1: 1, 0.5: 2, 0.9: pun.I(3,4), 1:5}

• std (number) – standard deviation of the variable

• var (number) – variance of the variable

• family (str) – name of the distribution family, e.g. ‘normal’, ‘lognormal’, ‘uniform’, ‘triangular’, etc.

Returns:

uncertain number

Note

It’s also possible to directly call a function given the known information, such as pun.mean_std(mean=1, std=0.5).

Example

>>> from pyuncertainnumber.pba import known_properties
>>> known_properties(
...     maximum = 2,
...     mean = 1,
...     var = 0.25,
...     minimum=0,
...     )

pyuncertainnumber.pba.pbox_free.known_constraints

pyuncertainnumber.pba.pbox_free.min_max(minimum: numbers.Number, maximum: numbers.Number) → pyuncertainnumber.characterisation.uncertainNumber.UncertainNumber | pyuncertainnumber.pba.pbox_abc.Pbox

Equivalent to an interval object constructed as a nonparametric Pbox.

Parameters:

• minimum – Left end of box

• maximum – Right end of box

Returns:

UncertainNumber or Pbox

Tip

Two types of return values are possible:

• by default, a UncertainNumber is returned;

• For low-level controls, if return_construct=True is specified, a Pbox is returned.

Example

>>> from pyuncertainnumber.pba import min_max
>>> min_max(0, 2)  # return a UncertainNumber
>>> min_max(0, 2, return_construct=True)  # return a Pbox

pyuncertainnumber.pba.pbox_free.min_mean(minimum, mean, steps=Params.steps) → pyuncertainnumber.characterisation.uncertainNumber.UncertainNumber | pyuncertainnumber.pba.pbox_abc.Pbox

Nonparametric pbox construction based on constraint of minimum and mean

Parameters:

• minimum (number) – minimum value of the variable

• mean (number) – mean value of the variable

Returns:

UncertainNumber or Pbox

Tip

Two types of return values are possible:

• by default, a UncertainNumber is returned;

• For low-level controls, if return_construct=True is specified, a Pbox is returned.

Example

>>> from pyuncertainnumber.pba import min_mean
>>> min_mean(0, 1)  # return a UncertainNumber
>>> min_mean(0, 1, return_construct=True)  # return a Pbox

pyuncertainnumber.pba.pbox_free.mean_std(mean: numbers.Number, std: numbers.Number, steps=Params.steps) → pyuncertainnumber.characterisation.uncertainNumber.UncertainNumber | pyuncertainnumber.pba.pbox_abc.Pbox

Nonparametric pbox construction based on constraint of mean and std

Parameters:

• mean (number) – mean value of the variable

• std (number) – std value of the variable

Returns:

UncertainNumber or Pbox

Tip

Two types of return values are possible:

• by default, a UncertainNumber is returned;

• For low-level controls, if return_construct=True is specified, a Pbox is returned.

Example

>>> mean_std(1, 0.5)

pyuncertainnumber.pba.pbox_free.mean_var(mean: numbers.Number, var: numbers.Number) → pyuncertainnumber.characterisation.uncertainNumber.UncertainNumber | pyuncertainnumber.pba.pbox_abc.Pbox

Nonparametric pbox construction based on constraint of mean and var

Parameters:

• mean (number) – mean value of the variable

• vasr (number) – var value of the variable

Returns:

UncertainNumber or Pbox

Tip

Two types of return values are possible:

• by default, a UncertainNumber is returned;

• For low-level controls, if return_construct=True is specified, a Pbox is returned.

Example

>>> mean_var(1, 0.25)  # return a UncertainNumber

pyuncertainnumber.pba.pbox_free.min_max_mean(minimum: numbers.Number, maximum: numbers.Number, mean: numbers.Number, steps: int = Params.steps) → pyuncertainnumber.characterisation.uncertainNumber.UncertainNumber | pyuncertainnumber.pba.pbox_abc.Pbox

Generates a distribution-free p-box based upon the minimum, maximum and mean of the variable

Parameters:

• minimum (float) – minimum value of the variable

• maximum (float) – maximum value of the variable

• mean (float) – mean value of the variable

Returns:

UncertainNumber or Pbox

Tip

Two types of return values are possible:

• by default, a UncertainNumber is returned;

• For low-level controls, if return_construct=True is specified, a Pbox is returned.

Example

>>> min_max_mean(0, 2, 1)

pyuncertainnumber.pba.pbox_free.pos_mean_std(mean: numbers.Number, std: numbers.Number, steps=Params.steps) → pyuncertainnumber.pba.pbox_abc.Pbox

Generates a positive distribution-free p-box based upon the mean and standard deviation of the variable

Parameters:

• mean – mean of the variable

• std – standard deviation of the variable

Returns:

UncertainNumber or Pbox

Tip

Two types of return values are possible:

• by default, a UncertainNumber is returned;

• For low-level controls, if return_construct=True is specified, a Pbox is returned.

pyuncertainnumber.pba.pbox_free.min_max_mode(minimum: numbers.Number, maximum: numbers.Number, mode: numbers.Number, steps: int = Params.steps) → pyuncertainnumber.characterisation.uncertainNumber.UncertainNumber | pyuncertainnumber.pba.pbox_abc.Pbox

Nonparametric pbox construction based on constraint of mean and var

Parameters:

• minimum – minimum value of the variable

• maximum – maximum value of the variable

• mode (number) – mode value of the variable

Returns:

UncertainNumber or Pbox

Tip

Two types of return values are possible:

• by default, a UncertainNumber is returned;

• For low-level controls, if return_construct=True is specified, a Pbox is returned.

Example

>>> min_max_mode(0, 2, 1)  # return a UncertainNumber

pyuncertainnumber.pba.pbox_free.min_max_median(minimum: numbers.Number, maximum: numbers.Number, median: numbers.Number, steps: int = Params.steps) → pyuncertainnumber.characterisation.uncertainNumber.UncertainNumber | pyuncertainnumber.pba.pbox_abc.Pbox

Generates a distribution-free p-box based upon the minimum, maximum and median of the variable

Parameters:

• minimum – minimum value of the variable

• maximum – maximum value of the variable

• median – median value of the variable

Returns:

UncertainNumber or Pbox

Tip

Two types of return values are possible:

• by default, a UncertainNumber is returned;

• For low-level controls, if return_construct=True is specified, a Pbox is returned.

Example

>>> min_max_median(0, 2, 1)  # return a UncertainNumber

pyuncertainnumber.pba.pbox_free.min_max_mean_std(minimum: numbers.Number, maximum: numbers.Number, mean: numbers.Number, std: numbers.Number, **kwargs) → pyuncertainnumber.characterisation.uncertainNumber.UncertainNumber | pyuncertainnumber.pba.pbox_abc.Pbox

Generates a distribution-free p-box based upon the minimum, maximum, mean and standard deviation of the variable

Parameters:

• maximum (number) – maximum value of the variable

• minimum (number) – minimum value of the variable

• std (number) – standard deviation of the variable

• var (number) – variance of the variable

Returns:

UncertainNumber or Pbox

Tip

Two types of return values are possible:

• by default, a UncertainNumber is returned;

• For low-level controls, if return_construct=True is specified, a Pbox is returned.

Example

>>> min_max_mean_std(0, 2, 1, 0.5)  # return a UncertainNumber

See also

min_max_mean_var()

pyuncertainnumber.pba.pbox_free.min_max_mean_var(minimum: numbers.Number, maximum: numbers.Number, mean: numbers.Number, var: numbers.Number, **kwargs) → pyuncertainnumber.characterisation.uncertainNumber.UncertainNumber | pyuncertainnumber.pba.pbox_abc.Pbox

Generates a distribution-free p-box based upon the minimum, maximum, mean and standard deviation of the variable

Parameters:

• minimum (number) – minimum value of the variable

• maximum (number) – maximum value of the variable

• mean (number) – mean value of the variable

• var (number) – variance of the variable

Tip

Two types of return values are possible:

• by default, a UncertainNumber is returned;

• For low-level controls, if return_construct=True is specified, a Pbox is returned.

Example

>>> min_max_mean_var(0, 2, 1, 0.25)  # return a UncertainNumber

Implementation

Equivalent to min_max_mean_std(minimum,maximum,mean,np.sqrt(var))

See also

min_max_mean_std()

pyuncertainnumber.pba.pbox_free.from_percentiles(percentiles: dict, steps: int = Params.steps) → pyuncertainnumber.characterisation.uncertainNumber.UncertainNumber | pyuncertainnumber.pba.pbox_abc.Pbox

yields a distribution-free p-box based on specified percentiles of the variable

Parameters:

• percentiles – dictionary of percentiles and their values (e.g. {0: 0, 0.1: 1, 0.5: 2, 0.9: I(3,4), 1:5})

• steps – number of steps to use in the p-box

Note

The percentiles dictionary is of the form {percentile: value}. Where value can either be a number or an I. If value is a number, the percentile is assumed to be a point percentile. If value is an I, the percentile is assumed to be an interval percentile. If no keys for 0 and 1 are given, -np.inf and np.inf are used respectively. This will result in a p-box that is not bounded and raise a warning. If the percentiles are not increasing, the percentiles will be intersected. This may not be desired behaviour. ValueError: If any of the percentiles are not between 0 and 1.

Returns:

UncertainNumber or Pbox

Tip

Two types of return values are possible:

• by default, a UncertainNumber is returned;

• For low-level controls, if return_construct=True is specified, a Pbox is returned.

Example

>>> pba.from_percentiles(
>>>     {0: 0,
>>>     0.25: 0.5,
>>>     0.5: pba.I(1,2),
>>>     0.75: pba.I(1.5,2.5),
>>>     1: 3})
>>>     .display()