gemseo.uncertainty.distributions.base_joint module#
Joint probability distribution.
The base class BaseJointDistribution
implements the concept of joint probability distribution.
The joint probability distribution of a set of random variables is the probability distribution of the random vector consisting of these random variables.
It takes into account both the marginal probability distributions of these random variables and their dependency structure.
A BaseJointDistribution is defined
from a list of BaseDistribution objects
defining the marginals of the random variables
and a copula defining the dependency structure between them.
Note
A copula is a mathematical function used to define the dependence between random variables from their cumulative distribution functions. See more.
By definition, a joint probability distribution is a probability distribution.
Therefore, BaseJointDistribution inherits
from the abstract class BaseDistribution.
The BaseJointDistribution of a list of given uncertain variables is built
from a list of BaseDistribution objects
implementing the probability distributions of these variables
and from a copula.
Because BaseJointDistribution inherits from BaseDistribution,
we can easily get statistics, such as mean,
standard_deviation.
We can also get the numerical range and
mathematical support.
Note
We call mathematical support the set of values that the random variable can take in theory, e.g. \(]-\infty,+\infty[\) for a Gaussian variable, and numerical range the set of values that it can take in practice, taking into account the values rounded to zero double precision. Both support and range are described in terms of lower and upper bounds
We can also evaluate the cumulative density function
(compute_cdf())
for the different marginals of the random variable,
as well as the inverse cumulative density function
(compute_inverse_cdf()).
Lastly, we can compute realizations of the random variable
by means of the compute_samples() method.
- class BaseJointDistribution(distributions, copula=None)[source]#
Bases:
BaseDistribution[ndarray[Any,dtype[floating[Any]]],Mapping[str,Any],Any]The base class for joint probability distributions.
The joint probability distribution of a random vector \(U=(U_1,\ldots,U_d)\) is characterized by the marginal probability distributions of \(U_1\), \(U_1\), ... and \(U_d\) and a copula used to describe the dependence between these \(d\) random variables.
Initialize self. See help(type(self)) for accurate signature.
- Parameters:
distributions (Sequence[BaseDistribution]) -- The marginal distributions.
copula (Any) -- A copula distribution defining the dependency structure between random variables; if
None, consider an independent copula.
- property marginals: Sequence[BaseDistribution]#
The marginal distributions.
- property range: ndarray[Any, dtype[floating[Any]]]#
The numerical range.
The numerical range is the interval defined by the lower and upper bounds numerically reachable by the random variable.