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 wasi
. Parameters
 nint or arraylike of ints
Number of experiments.
 pvalssequence 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 assum(pvals[:1]) <= 1)
. sizeint or tuple of ints, optional
Output shape. If the given shape is, e.g.,
(m, n, k)
, thenm * n * k
samples are drawn. Default is None, in which case a single value is returned.
 Returns
 outndarray
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 Ndimensional 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