bundles / numpy 2.5.0.dev0+git20251130.2de293a / numpy / random / _generator / Generator / multinomial

cython_function_or_method

`numpy.random._generator:Generator.multinomial`

Signature

def multinomial(n, pvals, size = None)

Summary

Draw samples from a multinomial distribution.

Extended Summary

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 : array-like of floats: Probabilities of each of the p different outcomes with shape (k0, k1, ..., kn, p). Each element pvals[i,j,...,:] must sum to 1 (however, the last element is always assumed to account for the remaining probability, as long as sum(pvals[..., :-1], axis=-1) <= 1.0. Must have at least 1 dimension where pvals.shape[-1] > 0.
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 each with p elements. Default is None where the output size is determined by the broadcast shape of n and all by the final dimension of pvals, which is denoted as b=(b0, b1, ..., bq). If size is not None, then it must be compatible with the broadcast shape b. Specifically, size must have q or more elements and size[-(q-j):] must equal bj.

Returns

out : ndarray

The drawn samples, of shape size, if provided. When size is provided, the output shape is size + (p,) If not specified, the shape is determined by the broadcast shape of n and pvals, (b0, b1, ..., bq) augmented with the dimension of the multinomial, p, so that that output shape is (b0, b1, ..., bq, p).

Each entry out[i,j,...,:] is a p-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([[3, 2, 2, 5, 4, 4]])

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([[2, 6, 4, 2, 2, 4],
       [2, 4, 6, 3, 3, 2]])

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, 2))

✗

array([[[2, 2, 1, 1, 1, 3],
        [2, 2, 1, 0, 3, 2]],

       [[4, 3, 2, 4, 4, 3],
        [4, 3, 8, 2, 1, 2]]])

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([12, 14, 18, 14, 15, 27])

Simulate 10 throws of a 4-sided die and 20 throws of a 6-sided die

rng.multinomial([10, 20],[[1/4]*4 + [0]*2, [1/6]*6])

✗

array([[2, 2, 3, 3, 0, 0],
       [1, 6, 3, 3, 3, 4]])

Generate categorical random variates from two categories where the first has 3 outcomes and the second has 2.

rng.multinomial(1, [[.1, .5, .4 ], [.3, .7, .0]])

✗

array([[0, 0, 1],
       [0, 1, 0]])

``argmax(axis=-1)`` is then used to return the categories.

pvals = [[.1, .5, .4 ], [.3, .7, .0]]
rvs = rng.multinomial(1, pvals, size=(4,2))

✓

rvs.argmax(axis=-1)

✗

array([[2, 0],
       [0, 1],
       [1, 1],
       [2, 0]])

The same output dimension can be produced using broadcasting.

rvs = rng.multinomial([[1]] * 4, pvals)

✓

rvs.argmax(axis=-1)

✗

array([[1, 0],
       [1, 1],
       [0, 0],
       [1, 1]])

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])

not like:

rng.multinomial(100, [1.0, 2.0])  # WRONG

✓

Traceback (most recent call last):
  File "<doctest numpy.random._generator:Generator.multinomial[0]>", line 1, in <module>
    rng.multinomial(100, [1.0, 2.0])  # WRONG
    ~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^
  File "numpy/random/_generator.pyx", line 4108, in numpy.random._generator.Generator.multinomial
  File "numpy/random/_common.pyx", line 393, in numpy.random._common.check_array_constraint
  File "numpy/random/_common.pyx", line 379, in numpy.random._common._check_array_cons_bounded_0_1
ValueError: pvals < 0, pvals > 1 or pvals contains NaNs