List of Multivariate Distributions

Multinomial

Multinomial distribution having probability mass function

f(x) = \dfrac{n!}{x_1!\dots x_k!}p_1^{x_1}\dots p_k^{x_k}

for x=\{x_1,\dots,x_k\} where each x_i is a non-negative integer and \sum_i x_i = n.

The :class:`.Multinomial` class is imported using the following command:

>>> from UQpy.distributions.collection.Multinomial import Multinomial

.. autoclass:: UQpy.distributions.collection.Multinomial
    :members:

The following methods are available for :class:`.Multinomial`:

Multivariate normal distribution having probability density function

f(x) = \dfrac{1}{\sqrt{(2\pi)^k\det\Sigma}}\exp{-\dfrac{1}{2}(x-\mu)^T\Sigma^{-1}(x-\mu)}

where \mu is the mean vector, \Sigma is the covariance matrix, and k is the dimension of x.

The :class:`.MultivariateNormal` class is imported using the following command:

>>> from UQpy.distributions.collection.MultivariateNormal import MultivariateNormal

.. autoclass:: UQpy.distributions.collection.MultivariateNormal
    :members:

The following methods are available for :class:`.MultivariateNormal` :