numpy.random.Generator.multinomial#
method
- random.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 array-like of ints
Number of experiments.
- pvalsarray-like of floats
Probabilities of each of the
p
different outcomes with shape(k0, k1, ..., kn, p)
. Each elementpvals[i,j,...,:]
must sum to 1 (however, the last element is always assumed to account for the remaining probability, as long assum(pvals[..., :-1], axis=-1) <= 1.0
. Must have at least 1 dimension where pvals.shape[-1] > 0.- sizeint or tuple of ints, optional
Output shape. If the given shape is, e.g.,
(m, n, k)
, thenm * n * k
samples are drawn each withp
elements. Default is None where the output size is determined by the broadcast shape ofn
and all by the final dimension ofpvals
, which is denoted asb=(b0, b1, ..., bq)
. If size is not None, then it must be compatible with the broadcast shapeb
. Specifically, size must haveq
or more elements and size[-(q-j):] must equalbj
.
- Returns
- outndarray
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
andpvals
,(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 ap
-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, 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
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, 1, 4, 3, 0, 0], [3, 3, 3, 6, 1, 4]], dtype=int64) # random
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]], dtype=int64) # random
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([[0, 1], [2, 0], [2, 1], [2, 0]], dtype=int64) # random
The same output dimension can be produced using broadcasting.
>>> rvs = rng.multinomial([[1]] * 4, pvals) >>> rvs.argmax(axis=-1) array([[0, 1], [2, 0], [2, 1], [2, 0]], dtype=int64) # 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