Parent Distribution Class

Methods

class Distribution(ordered_parameters=None, **kwargs)[source]

A parent class to all Distribution classes.

All distributions possess a number of methods to perform basic probabilistic operations. For most of the predefined distributions in UQpy these methods are inherited from the scipy.stats package. These include standard operations such as computing probability density/mass functions, cumulative distribution functions and their inverse, drawing random samples, computing moments and parameter fitting. However, for user-defined distributions, any desired method can be constructed into the child class structure.

For bookkeeping purposes, all Distribution objects possesses get_parameters() and update_parameters() methods. These are described in more detail below.

Any Distribution further inherits from one of the following classes:

  • DistributionContinuous1D: Parent class to 1-dimensional continuous probability distributions.

  • DistributionDiscrete1D: Parent class to 1-dimensional discrete probability distributions.

  • DistributionND: Parent class to multivariate probability distributions.

Parameters:
update_parameters(**kwargs)[source]

Update the parameters of a Distribution object.

To update the parameters of a JointIndependent or a JointCopula distribution, each parameter is assigned a unique string identifier as key_index - where key is the parameter name and index the index of the marginal (e.g., location parameter of the 2nd marginal is identified as loc_1).

Parameters:

kwargs (dict) – Parameters to be updated, designated by their respective keywords.

get_parameters()[source]

Return the parameters of a Distribution object.

To update the parameters of a JointIndependent or a JointCopula distribution, each parameter is assigned a unique string identifier as key_index - where key is the parameter name and index the index of the marginal (e.g., location parameter of the 2nd marginal is identified as loc_1).

Returns:

Parameters of the distribution.

Attributes

Distribution.parameters: dict

Ordered list of parameter names, useful when parameter values are stored in vectors and must be passed to the update_params() method.

Distribution.ordered_parameters: list

Parameters of the distribution.

This attribute is not defined for certain Distribution objects such as those of type JointIndependent or JointCopula. The user is advised to use the get_parameters() method to access the parameters.

Additional methods available from scipy.stats :

cdf(x)

Evaluate the cumulative distribution function.

Parameters:

x – Point(s) at which to evaluate the cdf(), must be numpy.ndarray of shape (npoints, dimension).

Returns:

Evaluated cdf values, numpy.ndarray of shape (npoints,).

pdf(x)

Evaluate the probability density function of a continuous or multivariate mixed continuous-discrete distribution.

Parameters:

x – Point(s) at which to evaluate the pdf(), must be numpy.ndarray of shape (npoints, dimension).

Returns:

Evaluated pdf values, numpy.ndarray of shape (npoints,).

pmf(x)

Evaluate the probability mass function of a discrete distribution.

Parameters:

x – Point(s) at which to evaluate the pmf(), must be numpy.ndarray of shape (npoints, dimension).

Returns:

Evaluated pmf values, numpy.ndarray of shape (npoints,).

log_pdf(x)

Evaluate the logarithm of the probability density function of a continuous or multivariate mixed continuous-discrete distribution.

Parameters:

x – Point(s) at which to evaluate the log_pdf(), must be numpy.ndarray of shape (npoints, dimension).

Returns:

Evaluated log-pdf values, numpy.ndarray of shape (npoints,).

log_pmf(x)

Evaluate the logarithm of the probability mass function of a discrete distribution.

Parameters:

x – Point(s) at which to evaluate the log_pmf(), must be numpy.ndarray of shape (npoints, dimension).

Returns:

Evaluated log-pmf values, numpy.ndarray of shape (npoints,).

icdf(x)

Evaluate the inverse cumulative distribution function for univariate distributions.

Parameters:

x – Point(s) at which to evaluate the icdf(), must be of shape (npoints, dimension).

Returns:

Evaluated icdf values, numpy.ndarray of shape (npoints,).

Return type:

numpy.ndarray

rvs(nsamples=1, random_state=None)

Sample independent identically distributed (iid) realizations.

Parameters:

  • nsamples – Number of iid samples to be drawn. Default is 1.

  • random_state – Random seed used to initialize the pseudo-random number generator. Default is None. If an int is provided, this sets the seed for an object of numpy.random.RandomState. Otherwise, the object itself can be passed directly.

Returns:

Generated iid samples, :class:`numpy.ndarray of shape (npoints, dimension).

moments(moments2return='mvsk')

Computes the mean (‘m’), variance/covariance (‘v’), skewness (‘s’) and/or kurtosis (‘k’) of the distribution. For a univariate distribution, mean, variance, skewness and kurtosis are returned. For a multivariate distribution, the mean vector, covariance and vectors of marginal skewness and marginal kurtosis are returned.

Parameters:

moments2return – Indicates which moments are to be returned (mean, variance, skewness and/or kurtosis). Default is ‘mvsk’.

Returns:

mean: mean, var: variance/covariance, skew: skewness, kurt: kurtosis.

Return type:

tuple

fit(data)

Compute the maximum-likelihood parameters from iid data. Computes the mle analytically if possible. For univariate continuous distributions, it leverages the fit method of the scipy.stats package.

Parameters:

data – Data array, must be numpy.ndarray of shape (npoints, dimension).

Returns:

Maximum-likelihood parameter estimates.

Return type:

dict