  The generation of pseudo-random discrete probability distributions is of
paramount importance for a wide range of stochastic simulations spanning from
Monte Carlo methods to the random sampling of quantum states for investigations
in quantum information science. In spite of its significance, a thorough
exposition of such a procedure is lacking in the literature. In this article we
present relevant details concerning the numerical implementation and
applicability of what we call the iid, normalization, and trigonometric methods
for generating an unbiased probability vector
$\mathbf{p}=(p_{1},\cdots,p_{d})$. An immediate application of these results
regarding the generation of pseudo-random pure quantum states is also
described.
