scipy.stats.dirichlet_multinomial — SciPy v1.15.3 Manual (original) (raw)

scipy.stats.dirichlet_multinomial = <scipy.stats._multivariate.dirichlet_multinomial_gen object>[source]#

A Dirichlet multinomial random variable.

The Dirichlet multinomial distribution is a compound probability distribution: it is the multinomial distribution with number of trials_n_ and class probabilities p randomly sampled from a Dirichlet distribution with concentration parameters alpha.

Parameters:

alphaarray_like

The concentration parameters. The number of entries along the last axis determines the dimensionality of the distribution. Each entry must be strictly positive.

nint or array_like

The number of trials. Each element must be a strictly positive integer.

seed{None, int, np.random.RandomState, np.random.Generator}, optional

Used for drawing random variates. If seed is None, the RandomState singleton is used. If seed is an int, a new RandomState instance is used, seeded with seed. If seed is already a RandomState or Generator instance, then that object is used. Default is None.

References

Examples

from scipy.stats import dirichlet_multinomial

Get the PMF

n = 6 # number of trials alpha = [3, 4, 5] # concentration parameters x = [1, 2, 3] # counts dirichlet_multinomial.pmf(x, alpha, n) 0.08484162895927604

If the sum of category counts does not equal the number of trials, the probability mass is zero.

dirichlet_multinomial.pmf(x, alpha, n=7) 0.0

Get the log of the PMF

dirichlet_multinomial.logpmf(x, alpha, n) -2.4669689491013327

Get the mean

dirichlet_multinomial.mean(alpha, n) array([1.5, 2. , 2.5])

Get the variance

dirichlet_multinomial.var(alpha, n) array([1.55769231, 1.84615385, 2.01923077])

Get the covariance

dirichlet_multinomial.cov(alpha, n) array([[ 1.55769231, -0.69230769, -0.86538462], [-0.69230769, 1.84615385, -1.15384615], [-0.86538462, -1.15384615, 2.01923077]])

Alternatively, the object may be called (as a function) to fix thealpha and n parameters, returning a “frozen” Dirichlet multinomial random variable.

dm = dirichlet_multinomial(alpha, n) dm.pmf(x) 0.08484162895927579

All methods are fully vectorized. Each element of x and alpha is a vector (along the last axis), each element of n is an integer (scalar), and the result is computed element-wise.

x = [[1, 2, 3], [4, 5, 6]] alpha = [[1, 2, 3], [4, 5, 6]] n = [6, 15] dirichlet_multinomial.pmf(x, alpha, n) array([0.06493506, 0.02626937])

dirichlet_multinomial.cov(alpha, n).shape # both covariance matrices (2, 3, 3)

Broadcasting according to standard NumPy conventions is supported. Here, we have four sets of concentration parameters (each a two element vector) for each of three numbers of trials (each a scalar).

alpha = [[3, 4], [4, 5], [5, 6], [6, 7]] n = [[6], [7], [8]] dirichlet_multinomial.mean(alpha, n).shape (3, 4, 2)

Methods