flopscope.numpy.random.dirichlet

Draw size samples of dimension k from a Dirichlet distribution. A Dirichlet-distributed random variable can be seen as a multivariate generalization of a Beta distribution. The Dirichlet distribution is a conjugate prior of a multinomial distribution in Bayesian inference.

alpha:sequence of floats, length k

Parameter of the distribution (length k for sample of length k).

size:int or tuple of ints, optional

Output shape. If the given shape is, e.g., (m, n), then m * n * k samples are drawn. Default is None, in which case a vector of length k is returned.

samples:ndarray,

The drawn samples, of shape (size, k).

:ValueError

If any value in alpha is less than or equal to zero

• we.flops.random.Generator.dirichlet which should be used for new code.

The Dirichlet distribution is a distribution over vectors $x$ that fulfil the conditions $x_i>0$ and $\sum_{i=1}^k x_i = 1$.

The probability density function $p$ of a Dirichlet-distributed random vector $X$ is proportional to

where $\alpha$ is a vector containing the positive concentration parameters.

The method uses the following property for computation: let $Y$ be a random vector which has components that follow a standard gamma distribution, then $X = \frac{1}{\sum_{i=1}^k{Y_i}} Y$ is Dirichlet-distributed

Taking an example cited in Wikipedia, this distribution can be used if one wanted to cut strings (each of initial length 1.0) into K pieces with different lengths, where each piece had, on average, a designated average length, but allowing some variation in the relative sizes of the pieces.