multinomial(n, pvals, size=None)¶
Draw samples from a multinomial distribution.
The multinomial distribution is a multivariate generalisation of the binomial distribution. Take an experiment with one of
ppossible 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
n : int
Number of experiments.
pvals : sequence of floats, length p
Probabilities of each of the
pdifferent outcomes. These should 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 * ksamples 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
In other words, each entry
out[i,j,...,:]is an N-dimensional value drawn from the distribution.
Throw a dice 20 times:
>>> np.random.multinomial(20, [1/6.]*6, size=1) array([[4, 1, 7, 5, 2, 1]])
It landed 4 times on 1, once on 2, etc.
Now, throw the dice 20 times, and 20 times again:
>>> np.random.multinomial(20, [1/6.]*6, size=2) array([[3, 4, 3, 3, 4, 3], [2, 4, 3, 4, 0, 7]])
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.
A loaded die is more likely to land on number 6:
>>> np.random.multinomial(100, [1/7.]*5 + [2/7.]) array([11, 16, 14, 17, 16, 26])
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:
>>> np.random.multinomial(100, [1.0 / 3, 2.0 / 3]) # RIGHT array([38, 62])
>>> np.random.multinomial(100, [1.0, 2.0]) # WRONG array([100, 0])