 The formula can be understood by noting that after the first "k" − 1 values have their portions assigned, the length of the remainder of the stick is formula_119 and this piece is broken according to formula_114 and gets assigned to formula_112.The smaller formula_2 is, the less of the stick will be left for subsequent values (on average), yielding more concentrated distributions.The stick breaking process is similar to the construction where one samples sequentially from marginal beta distributions in order to generate a sample from a Dirichlet distribution.