Merge pull request #12333 from tuelwer/master

DOC: update description of the Dirichlet distribution

1 files changed, 20 insertions, 8 deletions

diff --git a/numpy/random/mtrand/mtrand.pyx b/numpy/random/mtrand/mtrand.pyx
index e4a401b24..2a6daa88c 100644
--- a/numpy/random/mtrand/mtrand.pyx
+++ b/numpy/random/mtrand/mtrand.pyx
@@ -4673,8 +4673,9 @@ cdef class RandomState:
 
         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.
+        generalization of a Beta distribution. The Dirichlet distribution
+        is a conjugate prior of a multinomial distribution in Bayesian 
+        inference.
 
         Parameters
         ----------
@@ -4698,13 +4699,24 @@ cdef class RandomState:
 
         Notes
         -----
-        .. math:: X \\approx \\prod_{i=1}^{k}{x^{\\alpha_i-1}_i}
 
-        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
-        :math:`X = \\frac{1}{\\sum_{i=1}^k{y_i}} (y_1, \\ldots, y_n)` is
-        Dirichlet distributed.
+        The Dirichlet distribution is a distribution over vectors 
+        :math:`x` that fulfil the conditions :math:`x_i>0` and 
+        :math:`\\sum_{i=1}^k x_i = 1`.
+
+        The probability density function :math:`p` of a 
+        Dirichlet-distributed random vector :math:`X` is 
+        proportional to
+
+        .. math:: p(x) \\propto \\prod_{i=1}^{k}{x^{\\alpha_i-1}_i},
+
+        where :math:`\\alpha` is a vector containing the positive 
+        concentration parameters.
+
+        The method uses the following property for computation: let :math:`Y`
+        be a random vector which has components that follow a standard gamma 
+        distribution, then :math:`X = \\frac{1}{\\sum_{i=1}^k{Y_i}} Y` 
+        is Dirichlet-distributed
 
         References
         ----------