Draw samples from the Dirichlet distribution.
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. Dirichlet pdf is the conjugate
prior of a multinomial in Bayesian inference.
Parameters : | alpha : array
Parameter of the distribution (k dimension for sample of
dimension k).
size : array
Number of samples to draw.
|
Returns : | samples : ndarray,
The drawn samples, of shape (alpha.ndim, size).
|
Notes
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Transcript written on math.log.
Uses the following property for computation: for each dimension,
draw a random sample y_i from a standard gamma generator of shape
alpha_i, then
System Message: WARNING/2 (X = \frac{1}{\sum_{i=1}^k{y_i}} (y_1, \ldots, y_n))
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This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/TeX Live for SUSE Linux)
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(/usr/share/texmf/tex/latex/base/inputenc.sty
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Transcript written on math.log.
is
Dirichlet distributed.
References
Examples
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.
>>> s = np.random.dirichlet((10, 5, 3), 20).transpose()
>>> plt.barh(range(20), s[0])
>>> plt.barh(range(20), s[1], left=s[0], color='g')
>>> plt.barh(range(20), s[2], left=s[0]+s[1], color='r')
>>> plt.title("Lengths of Strings")