distribution module¶
The interface to SciPy-based probability distributions.
The SPDistribution
class is a concrete class
inheriting from Distribution
which is an abstract one.
SP stands for scipy
which is the library it relies on.
The SPDistribution
of a given uncertain variable is built
from mandatory arguments:
a variable name,
a distribution name recognized by SciPy,
a set of parameters provided as a dictionary of keyword arguments named as the arguments of the scipy constructor of this distribution.
Warning
The distribution parameters must be provided according to the signature of the scipy classes. Access the scipy documentation.
The constructor has also optional arguments:
a variable dimension (default: 1),
a standard representation of these parameters (default: use
parameters
).
- class gemseo.uncertainty.distributions.scipy.distribution.SPDistribution(variable='x', interfaced_distribution='uniform', parameters=mappingproxy({}), dimension=1, standard_parameters=None)[source]
Bases:
Distribution
A SciPy-based probability distribution.
Create a probability distribution for an uncertain variable from its dimension and distribution names and properties.
See also
SPExponentialDistribution
SPNormalDistribution
SPTriangularDistribution
SPUniformDistribution
Examples
>>> from gemseo.uncertainty.distributions.scipy.distribution import ( ... SPDistribution, ... ) >>> distribution = SPDistribution("x", "expon", {"loc": 3, "scale": 1 / 2.0}) >>> print(distribution) expon(loc=3, scale=0.5)
- Parameters:
variable (str) –
The name of the random variable.
By default it is set to “x”.
interfaced_distribution (str) –
The name of the probability distribution, typically the name of a class wrapped from an external library, such as
"Normal"
for OpenTURNS or"norm"
for SciPy.By default it is set to “uniform”.
parameters (Mapping[str, Any]) –
The parameters of the probability distribution.
By default it is set to {}.
dimension (int) –
The dimension of the random variable. If greater than 1, the probability distribution is applied to all components of the random variable under the hypothesis that these components are stochastically independent. To be removed in a future version; use a
ComposedDistribution
instead.By default it is set to 1.
standard_parameters (StandardParametersType | None) – The parameters of the probability distribution used for string representation only (use
parameters
for computation). IfNone
, useparameters
instead. For instance, let us consider the interfaced SciPy distribution"uniform"
. Then, the string representation ofSPDistribution("x", "uniform", parameters, 1, {"min": 1, "max": 3})
withparameters={"loc": 1, "scale": 2}
is"uniform(max=3, min=1)"
while the string representation ofSPDistribution("x", "uniform", parameters)
is"uniform(loc=1, scale=2)"
.
- COMPOSED_DISTRIBUTION_CLASS
alias of
SPComposedDistribution
- compute_cdf(vector)[source]
Evaluate the cumulative density function (CDF).
Evaluate the CDF of the components of the random variable for a given realization of this random variable.
- Parameters:
vector (Iterable[float]) – A realization of the random variable.
- Returns:
The CDF values of the components of the random variable.
- Return type:
ndarray
- compute_inverse_cdf(vector)[source]
Evaluate the inverse of the cumulative density function (ICDF).
- Parameters:
vector (Iterable[float]) – A vector of values comprised between 0 and 1 whose length is equal to the dimension of the random variable.
- Returns:
The ICDF values of the components of the random variable.
- Return type:
ndarray
- compute_samples(n_samples=1, random_state=None)[source]
Sample the random variable.
- Parameters:
- Returns:
The samples of the random variable,
The number of columns is equal to the dimension of the variable and the number of lines is equal to the number of samples.
- Return type:
ndarray
- dimension: int
The number of dimensions of the random variable.
- distribution: type
The probability distribution of the random variable.
- distribution_name: str
The name of the probability distribution.
- math_lower_bound: ndarray
The mathematical lower bound of the random variable.
- math_upper_bound: ndarray
The mathematical upper bound of the random variable.
- property mean: ndarray
The analytical mean of the random variable.
- num_lower_bound: ndarray
The numerical lower bound of the random variable.
- num_upper_bound: ndarray
The numerical upper bound of the random variable.
- property standard_deviation: ndarray
The analytical standard deviation of the random variable.
- standard_parameters: dict[str, str] | None
The standard representation of the parameters of the distribution, used for its string representation.
- transformation: str
The transformation applied to the random variable, e.g. ‘sin(x)’.
- variable_name: str
The name of the random variable.
Examples using SPDistribution¶
Probability distributions based on SciPy