The alpha keyword specifies the concentration parameters of the distribution.

Each \alpha entry must be positive. The distribution has only support on the simplex defined by

where 0 < x_i < 1.

If the quantiles don't lie within the simplex, a ValueError is raised.

The probability density function for dirichlet is

where

\mathrm{B}(\boldsymbol\alpha) = \frac{\prod_{i=1}^K \Gamma(\alpha_i)}
                             {\Gamma\bigl(\sum_{i=1}^K \alpha_i\bigr)}

and \boldsymbol\alpha=(\alpha_1,\ldots,\alpha_K), the concentration parameters and K is the dimension of the space where x takes values.

Note that the dirichlet interface is somewhat inconsistent. The array returned by the rvs function is transposed with respect to the format expected by the pdf and logpdf.

A Dirichlet random variable.

import numpy as np
from scipy.stats import dirichlet

quantiles = np.array([0.2, 0.2, 0.6])  # specify quantiles
alpha = np.array([0.4, 5, 15])  # specify concentration parameters
dirichlet.pdf(quantiles, alpha)

dirichlet.logpdf(quantiles, alpha)

dirichlet.mean(alpha)  # get the mean of the distribution

dirichlet.var(alpha) # get variance

dirichlet.entropy(alpha)  # calculate the differential entropy

dirichlet.rvs(alpha, size=1, random_state=1)

dirichlet.rvs(alpha, size=2, random_state=2)

rv = dirichlet(alpha)
# Frozen object with the same methods but holding the given
# concentration parameters fixed.