# Multinomial¶

class paddle.distribution. Multinomial ( total_count, probs ) [source]

Multinomial distribution parameterized by total_count and probs.

In probability theory, the multinomial distribution is a generalization of the binomial distribution, it models the probability of counts for each side of a k-sided die rolled n times. When k is 2 and n is 1, the multinomial is the bernoulli distribution, when k is 2 and n is grater than 1, it is the binomial distribution, when k is grater than 2 and n is 1, it is the categorical distribution.

The probability mass function (PMF) for multinomial is

$f(x_1, ..., x_k; n, p_1,...,p_k) = \frac{n!}{x_1!...x_k!}p_1^{x_1}...p_k^{x_k}$

where, $$n$$ is number of trials, k is the number of categories, $$p_i$$ denote probability of a trial falling into each category, $${\textstyle \sum_{i=1}^{k}p_i=1}, p_i \ge 0$$, and $$x_i$$ denote count of each category.

Parameters
• total_count (int) – Number of trials.

• probs (Tensor) – Probability of a trial falling into each category. Last axis of probs indexes over categories, other axes index over batches. Probs value should between [0, 1], and sum to 1 along last axis. If the value over 1, it will be normalized to sum to 1 along the last axis.

Examples:

import paddle

print(multinomial.sample((2, 3)))
# Tensor(shape=[2, 3, 3], dtype=float32, place=Place(gpu:0), stop_gradient=True,
#        [[[1., 4., 5.],
#          [0., 2., 8.],
#          [2., 4., 4.]],

#         [[1., 6., 3.],
#          [3., 3., 4.],
#          [3., 4., 3.]]])

probs ( value )

Probability density/mass function.

Note

This method will be deprecated in the future, please use prob instead.

property mean

mean of multinomial distribuion.

Returns

mean value.

Return type

Tensor

property variance

variance of multinomial distribution.

Returns

variance value.

Return type

Tensor

prob ( value )

probability mass function evaluated at value.

Parameters

value (Tensor) – value to be evaluated.

Returns

probability of value.

Return type

Tensor

log_prob ( value )

probability mass function evaluated at value

Parameters

value (Tensor) – value to be evaluated.

Returns

probability of value.

Return type

Tensor

sample ( shape=() )

draw sample data from multinomial distribution

Parameters

sample_shape (tuple, optional) – [description]. Defaults to ().

entropy ( )

entropy of multinomial distribution

Returns

entropy value

Return type

Tensor

property batch_shape

Returns batch shape of distribution

Returns

batch shape

Return type

Sequence[int]

property event_shape

Returns event shape of distribution

Returns

event shape

Return type

Sequence[int]

kl_divergence ( other ) [source]

The KL-divergence between self distributions and other.

rsample ( shape=() )

reparameterized sample