# numpy.random.Generator.multinomial¶

method

Generator.multinomial(n, pvals, size=None)

Draw samples from a multinomial distribution.

The multinomial distribution is a multivariate generalization of the binomial distribution. Take an experiment with one of p possible outcomes. An example of such an experiment is throwing a dice, where the outcome can be 1 through 6. Each sample drawn from the distribution represents n such experiments. Its values, X_i = [X_0, X_1, ..., X_p], represent the number of times the outcome was i.

Parameters: n : int or array-like of ints Number of experiments. pvals : sequence of floats, length p Probabilities of each of the p different outcomes. These must sum to 1 (however, the last element is always assumed to account for the remaining probability, as long as sum(pvals[:-1]) <= 1). size : int or tuple of ints, optional Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. Default is None, in which case a single value is returned. out : ndarray The drawn samples, of shape size, if that was provided. If not, the shape is (N,). In other words, each entry out[i,j,...,:] is an N-dimensional value drawn from the distribution.

Examples

Throw a dice 20 times:

>>> rng = np.random.default_rng()
>>> rng.multinomial(20, [1/6.]*6, size=1)
array([[4, 1, 7, 5, 2, 1]])  # random

It landed 4 times on 1, once on 2, etc.

Now, throw the dice 20 times, and 20 times again:

>>> rng.multinomial(20, [1/6.]*6, size=2)
array([[3, 4, 3, 3, 4, 3],
[2, 4, 3, 4, 0, 7]])  # random

For the first run, we threw 3 times 1, 4 times 2, etc. For the second, we threw 2 times 1, 4 times 2, etc.

Now, do one experiment throwing the dice 10 time, and 10 times again, and another throwing the dice 20 times, and 20 times again:

>>> rng.multinomial([[10], [20]], [1/6.]*6, size=2)
array([[[2, 4, 0, 1, 2, 1],
[1, 3, 0, 3, 1, 2]],
[[1, 4, 4, 4, 4, 3],
[3, 3, 2, 5, 5, 2]]])  # random

The first array shows the outcomes of throwing the dice 10 times, and the second shows the outcomes from throwing the dice 20 times.

A loaded die is more likely to land on number 6:

>>> rng.multinomial(100, [1/7.]*5 + [2/7.])
array([11, 16, 14, 17, 16, 26])  # random

The probability inputs should be normalized. As an implementation detail, the value of the last entry is ignored and assumed to take up any leftover probability mass, but this should not be relied on. A biased coin which has twice as much weight on one side as on the other should be sampled like so:

>>> rng.multinomial(100, [1.0 / 3, 2.0 / 3])  # RIGHT
array([38, 62])  # random

not like:

>>> rng.multinomial(100, [1.0, 2.0])  # WRONG
Traceback (most recent call last):
ValueError: pvals < 0, pvals > 1 or pvals contains NaNs

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