scipy.stats.dirichlet_multinomial#
- 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 parametersalpha
.- 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 aRandomState
orGenerator
instance, then that object is used. Default is None.
Methods
logpmf(x, alpha, n):
Log of the probability mass function.
pmf(x, alpha, n):
Probability mass function.
mean(alpha, n):
Mean of the Dirichlet multinomial distribution.
var(alpha, n):
Variance of the Dirichlet multinomial distribution.
cov(alpha, n):
The covariance of the Dirichlet multinomial distribution.
See also
scipy.stats.dirichlet
The dirichlet distribution.
scipy.stats.multinomial
The multinomial distribution.
References
[1]Dirichlet-multinomial distribution, Wikipedia, https://www.wikipedia.org/wiki/Dirichlet-multinomial_distribution
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 the
alpha
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)