pymc.Multinomial

class pymc.Multinomial(name, *args, **kwargs)

Multinomial log-likelihood.

Generalizes binomial distribution, but instead of each trial resulting in “success” or “failure”, each one results in exactly one of some fixed finite number k of possible outcomes over n independent trials. ‘x[i]’ indicates the number of times outcome number i was observed over the n trials.

\[f(x \mid n, p) = \frac{n!}{\prod_{i=1}^k x_i!} \prod_{i=1}^k p_i^{x_i}\]

Support	\(x \in \{0, 1, \ldots, n\}\) such that \(\sum x_i = n\)
Mean	\(n p_i\)
Variance	\(n p_i (1 - p_i)\)
Covariance	\(-n p_i p_j\) for \(i \ne j\)

Parameters:

ntensor_like of int

Total counts in each replicate (n > 0).

ptensor_like of float

Probability of each one of the different outcomes (0 <= p <= 1). The number of categories is given by the length of the last axis. Elements are expected to sum to 1 along the last axis.

Methods

Multinomial.dist(n, p, *args, **kwargs)

Creates a tensor variable corresponding to the cls distribution.