Editing Multinomial distribution (section)

=== Random variate generation ===
{{further|Non-uniform random variate generation}}

First, reorder the parameters <math>p_1, \ldots, p_k</math> such that they are sorted in descending order (this is only to speed up computation and not strictly necessary). Now, for each trial, draw an auxiliary variable ''X'' from a uniform (0,&nbsp;1) distribution. The resulting outcome is the component

: <math>j = \min \left\{ j' \in \{1,\dots,k\}\colon \left(\sum_{i=1}^{j'} p_i\right) - X \geq 0 \right\}.</math>

{''X''<sub>''j''</sub> = 1, ''X''<sub>''k''</sub> = 0 for ''k''&nbsp;≠&nbsp;''j'' } is one observation from the multinomial distribution with <math>p_1, \ldots, p_k</math> and ''n''&nbsp;=&nbsp;1.  A sum of independent repetitions of this experiment is an observation from a multinomial distribution with ''n'' equal to the number of such repetitions.