pyuncertainnumber.pba.distributions¶

Attributes¶

named_dists

Classes¶

`Distribution`	Two signatures are currentlly supported, either a parametric specification or from a nonparametric empirical data set.
`JointDistribution`	Joint distribution class
`ECDF`	Empirical cumulative distribution function (ecdf) class
`LognormalSaneDist`
`WrapperDist`

Functions¶

`uniform_sane`(a, b)
`lognormal_sane`(mu, sigma)	The sane lognormal which creates a lognormal distribution object based on the mean (mu) and standard deviation (sigma)
`expon_sane`(lamb)	Sane exponential distribution constructor

Module Contents¶

class pyuncertainnumber.pba.distributions.Distribution¶

Bases: pyuncertainnumber.pba.mixins.NominalValueMixin

Two signatures are currentlly supported, either a parametric specification or from a nonparametric empirical data set.

Note

the nonparametric instasntiation via arrtribute empirical_data will be deprecated soon. We have introduced a distributions.ECDF class instead.

Example

>>> d = Distribution('gaussian', (0,1))

dist_family: str = None¶

dist_params: list[float] | tuple[float, Ellipsis] = None¶

empirical_data: list[float] | numpy.ndarray = None¶

skip_post: bool = False¶

__post_init__()¶

__repr__()¶

rep()¶: Create the underling dist object either sps dist or sample approximated or pbox dist

Note

underlying constructor to create the scipy.stats distribution object

_match_distribution()¶: match the distribution object based on the family and parameters

parse_params_from_dist()¶

flag()¶

boolean flag for if the distribution is a parameterised distribution or not .. note:

- only parameterised dist can do sampling
- for non-parameterised sample-data based dist, next steps could be fitting

sample(size)¶: generate deviates from the distribution

generate_rns(N)¶: generate ‘N’ random numbers from the distribution

alpha_cut(alpha)¶: alpha cut interface

make_nominal_value()¶: one value representation of the distribution .. note:: - use mean for now;

plot(**kwargs)¶: display the distribution

display(**kwargs)¶

_get_hint()¶

fit(data)¶: fit the distribution to the data

get_PI(alpha: numbers.Number = 0.95) → pyuncertainnumber.Interval¶

Compute the predictive interval at the coverage level of alpha

Parameters:: alpha (-) – coverage level, default is 0.95

Example

>>> from pyuncertainnumber import pba
>>> d = pba.Distribution('gaussian', (0, 1))
>>> pi = d.get_PI(alpha=0.95)
>>> print(pi)  # prints the interval at the 95% coverage level

pdf(x: numpy.typing.ArrayLike)¶: compute the probability density function (pdf) at x

log_pdf_eval(x: numpy.typing.ArrayLike)¶: compute the log of probability density function (pdf) at x

cdf(x: numpy.typing.ArrayLike)¶: compute the cumulative distribution function (cdf) at x

get_whole_cdf()¶: return the cumulative distribution function (cdf)

_compute_nominal_value()¶

property dist¶: the underlying sps.dist object

property lo¶

property hi¶

property range¶

property hint¶

classmethod dist_from_sps(dist: scipy.stats.rv_continuous | scipy.stats.rv_discrete, shape: str = None)¶

to_pbox()¶

convert the distribution to a pbox .. note:

- this only works for parameteried distributions for now
- later on work with sample-approximated dist until `fit()`is implemented

__neg__()¶

__add__(other)¶

__radd__(other)¶

__sub__(other)¶

__rsub__(other)¶

__mul__(other)¶

__rmul__(other)¶

__truediv__(other)¶

__rtruediv__(other)¶

__pow__(other)¶

__rpow__(other)¶

class pyuncertainnumber.pba.distributions.JointDistribution(copula: pyuncertainnumber.pba.dependency.Dependency, marginals: list[Distribution])¶

Joint distribution class

Example

>>> from pyuncertainnumber import pba
>>> dist_a, dist_b = pba.Distribution('gaussian', (5,1)), pba.Distribution('uniform', (2, 3))
>>> c = pba.Dependency('gaussian', params=0.8)
>>> joint_dist = pba.JointDistribution(copula=c, marginals=[dist_a, dist_b])
>>> samples = joint_dist.sample(size=1000)

marginals¶

copula¶

_joint_dist¶

ndim¶

__repr__()¶

static from_sps(copula: statsmodels.distributions.copula, marginals: list[scipy.stats.rv_continuous])¶

sample(size, random_state=42)¶: generate orginal-space samples from the joint distribution

u_sample(size, random_state=42)¶: generate copula-space samples from the joint distribution

joint_density_of_bi_grid(x: numpy.typing.ArrayLike, y: numpy.typing.ArrayLike)¶

compute the joint density on a grid given x and y arrays

Used for bivariate arithmetic calculations of X and Y with designated (known) dependency and marginals.

Note

discretisation step sizes dx and dy are set up by the input x and y arrays

Example

>>> x = np.linspace(0, 1, 50)
>>> y = np.linspace(0, 1, 50)
>>> dep = Dependency("gaussian", params=0.7)
>>> joint_density = dep.joint_density_of_grid(x, y)

static cdf_of_g(XX, YY, fXY, dx, dy, g_func, z_vals) → numpy.typing.ArrayLike¶

Numerically approximate F_Z(z) = P(g(X,Y) <= z) via discretisation on a grid

Parameters:

z_vals (ArrayLike) – discretisation of z values (array) at which to compute F_Z
XX – the grid arrays from meshgrid
YY – the grid arrays from meshgrid
fXY – joint density on the grid
dx – spacings in x and y directions
dy – spacings in x and y directions
g_func (callable) – a general callable applied elementwise to (XX, YY)

Returns:

cumulative distribution function values at z_vals

Return type:

FZ (ArrayLike)

Note

given precomputed grid (XX,YY), joint density fXY, and spacings.

class pyuncertainnumber.pba.distributions.ECDF(empirical_data: numpy.ndarray)¶

Bases: pyuncertainnumber.pba.pbox_abc.Staircase

Empirical cumulative distribution function (ecdf) class

Implementation

supported by Pbox API hence samples will be degenerate intervals

Example

>>> import numpy as np
>>> s = np.random.normal(size=1000)
>>> ecdf = ECDF(s)
>>> ecdf.plot()

pyuncertainnumber.pba.distributions.uniform_sane(a, b)¶

pyuncertainnumber.pba.distributions.lognormal_sane(mu, sigma)¶

The sane lognormal which creates a lognormal distribution object based on the mean (mu) and standard deviation (sigma) of the underlying normal distribution.

Parameters:

mu (-) – Mean of the underlying normal distribution
sigma (-) – Standard deviation of the underlying normal distribution

Returns:

A scipy.stats.lognorm frozen distribution object

class pyuncertainnumber.pba.distributions.LognormalSaneDist¶

ppf(p_values, *params)¶

stats(*params, moments='mv')¶

pyuncertainnumber.pba.distributions.expon_sane(lamb)¶: Sane exponential distribution constructor

class pyuncertainnumber.pba.distributions.WrapperDist(ppf_func)¶

_ppf¶

ppf(*args, **kwargs)¶

pyuncertainnumber.pba.distributions.named_dists¶